Q: Cross-multiplication is a quick, easy way of solving rational equations. Unfortunately, this method only works for rational equations that contain exactly one rational expression or fraction on each side of the equals sign. If your equation isn't in proper cross-multiplication form, you may need to use algebraic operations to move its terms into their proper places. For instance, the equation (x + 3)/4 - x/(-2) = 0 can easily be rearranged into cross-multiplication form by adding x/(-2) to both sides of the equation, leaving you with (x + 3)/4 = x/(-2). Keep in mind that decimals and whole numbers can be made into fractions by giving them a denominator of 1. (x + 3)/4 - 2.5 = 5, for instance, can be rewritten as (x + 3)/4 = 7.5/1, making it a valid candidate for cross-multiplication. Some rational equations can't easily be reduced into a form with one fraction or rational equation on each side of the equals sign. In such cases, use a lowest common denominator approach. Cross-multiplication simply means multiplying one fraction's numerator by the other's denominator and vice versa. Multiply the numerator of the fraction on the left of the equal sign by the denominator of the fraction on the right. Repeat with the numerator of the right-hand fraction and the denominator of the fraction on the left. Cross-multiplication works according to basic algebraic principals. Rational expressions and other fractions can be made into non-fractions by multiplying them by their denominators. Cross-multiplication is basically a handy shortcut for multiplying both sides of the equation by both fraction's denominators. Don't believe it? Try it - you'll get the same results after simplifying. After cross-multiplying, you'll have two products. Set these two terms equal to each other and simplify to get each side of the equation in its simplest terms. For example, if your original rational expression was (x+3)/4 = x/(-2), after cross multiplying, your new equation is -2(x+3) = 4x. If we wish, this can also be written as -2x - 6 = 4x. Use algebraic operations to solve for the variable in your equation. Remember that, if x appears on both sides of the equals sign, you'll need to add or subtract x terms to both sides to get x terms on only one side of the equals sign. In our example, we can divide both sides of the equation by -2, giving us x+3 = -2x. Subtracting x from both sides gives us 3 = -3x. Finally, dividing both sides by -3 gives us -1 = x, which we can re-write as x = -1. We have found x, solving our rational equation.
A: If necessary, rearrange your equation to get one fraction on each side of the equals sign. Cross-multiply. Set the two products as equal to each other. Solve for your variable.

Q: You can use a variety of fabric decors and trims available to decorate your toddler's basic white duvet. If you want to go with graphic designs, do not overload the duvet with a lot of it because then, it would look disorganized and loud. Simple, one-theme graphic designs are best. If applying trims to the duvet, make sure that all trims are straight and aligned along the sides of the mattress (not the duvet itself) as you will want to create depth when applying these trims to the duvet. You can also use piping, lace, jewelry, cord, tassel trims or the more playful venice trims. Most of these trims need to be machine sewn or if you have the time, hand stitched to the fabric rather than applying them using fabric glue. Stitching the trims makes it more durable, as machine washing the fabrics will remove the fabric glue. Check the alignment of your trims make the bed and cover it with the duvet you have embellished with the trims. Make sure that the outside edges of the trim details are straight and aligned with the edge of the mattress and the toddler bed. You can choose pillow covers that will compliment the style of the duvet you made or choose pillow covers in basic solid colors. For example, if you have chosen aqua for the bed frame, then you can use light yellow pillow covers or white pillow covers with yellow trims or decors. If you've chosen plum for the bed frame, you can partner it with ivory or white and brown duvet or bed covers and pillows with brown or ivory details. A bedside table that has the same or complimentary color to the bed frame, a stylish lamp, a wall clock and a bookcase are the basic things you need to complete the look. If your toddler bed has a head board, this is another canvas that you can use for your creative mind. You can either leave it wearing the solid color you gave the bed frame or you can also add details like stencils or pictures of your toddler or pictures of his favorite things. If your toddler's bed doesn't have a head board already, you can use a bookcase that fits the width of the bed; this pulls double duty in being a head board and a place to stow away toys or books or stuffed animals, which your toddler has easy access to.
A: Embellish the duvet. Embellish the pillow cover or the pillow. Add the decorations. Add a head board.

Q: Turn the hot plate on and let the beaker heat up gradually so that the thermal shock doesn't cause it to shatter. Wrap the mud in the towels and soak the mud in alcohol. The mud will take on the appearance of metal and will be 99 percent pure if you performed the process correctly. You can then take it to a jeweler or to a precious metals dealer to exchange it for cash if you desire.
A: Place your beaker onto a hot plate. Continue heating the mud until it develops a powder-like consistency. Pour the mud onto multiple layers of paper towels. Place the mud into a graphite crucible and melt it. Pour the gold into an ingot mold.

Q: As you start working, drink one of the caffeinated beverages you have set aside. Drink it slowly, so the caffeine doesn't overwhelm your system and cause you to crash. For every caffeinated beverage you drink, drink a cup of water. As the night goes on, increase the time between caffeinated beverages. If you feel yourself falling into a slump, take a multivitamin. No matter how focused you are, at some point, your brain will hit a wall. Instead of working through the slump at your computer, use this time to get in some exercise. A quick workout can boost your brain's ability to learn and retain information, which will help you break through your slump. Don't do a full workout instead, do some quick exercise in the form of 10 pushups, 10 jumping jacks or 10 sit ups. Pain stimulates the brain and keeps you from falling asleep. When you feel yourself nodding off, try pinching your thigh or eyebrow to give yourself a quick jolt. If pinching isn't cutting it, splash cold water on your face for an added boost. Lower the thermostat in your house or study area to keep your body alert. Take a cold shower to freeze yourself awake. Melatonin, the hormone that makes humans sleepy, is brought on by darkness, so turn on your brightest lights. Try to work in a room with fluorescent lighting, if possible. The closer the light is to your eyes, the better, so try to work near a desk lamp or computer screen. Change rooms every couple of hours so your eyes don't have time to fully adjust to the bright lights. Mint increases brain activity and improves memory, so chewing gum and sucking on mint candies can help you increase your alertness and improve the quality of your work. Keep a stash close to your desk and dip into it whenever you feel yourself slowing down. Drinking mint tea is also a great way to get some added caffeine.
A:
Begin your caffeine cycle. Take a break for exercise. Keep from falling asleep by making yourself uncomfortable. Keep the lights turned on. Chew gum.