INPUT ARTICLE: Article: Fall is a great time to play with fashionable jackets and coats. The weather is often just cold enough to warrant wearing one, but not so cold that you have to bundle up in the heavy, frumpy coats associated with winter. Pea coats are often made of wool and have a button-down front. They come in a variety of colors, ranging from black to red to olive green. These jackets create a slightly more masculine image. They look heavy and insulated, but many are still light enough to work well for fluctuating autumn weather. If you plan on keeping your look casual for the day, consider a hooded sweatshirt. Opt for fitted styles with a zipper front over pull-over types that have a tendency to look oversized and frumpy. Leather jackets come in a number of styles, from heavy and masculine to sleek and sexy. These pieces are also long-lasting and timeless, so you can often wear them year after year. On a warmer day with little wind, you may not need anything more than a feminine cardigan to keep you warm. Choose darker colors that look more fall-appropriate over white and pastel, which are generally associated with spring.

SUMMARY: Go for a mix of style and warmth. Consider a fitted pea coat. Look for bomber jackets or military jackets. Wear a fitted hoodie on casual days. Try leather. Consider a cardigan for warmer days.

In one sentence, describe what the following article is about: Lowest Common Denominators (LCD's) can be used to simplify rational equations, making it possible to solve for their variables. Finding an LCD is a good idea when your rational equation can't easily be written in a form that has one (and only one) fraction or rational expression on each side of the equals sign. For solving rational equations with three terms or more, LCD's are a helpful tool. However, for solving rational equations with only two terms, cross-multiplication can be faster. Identify the lowest number that each denominator divides into evenly. This is the LCD for your equation. Sometimes the lowest common denominator - that is, the lowest number that has each of the existing denominators as a factor - is obvious. For example, if your expression is x/3 + 1/2 = (3x+1)/6, it's not hard to see that the smallest number with 3, 2 and 6 as a factor, is, in fact, 6. Often, however, a rational equation's LCD isn't immediately obvious. In these cases, try examining multiples of the larger denominator until you find one that contains all of the smaller denominators as a factor. Often, the LCD is a multiple of two of the denominators. For example, in the equation x/8 + 2/6 = (x - 3)/9, the LCD is 8*9 = 72. If one or more of your fractions' denominators contains a variable, this process is more involved, but not impossible. In these cases, the LCD will be an expression (containing variables) that all the denominators divide into, not a single number. For example, in the equation 5/(x-1) = 1/x + 2/(3x), the LCD is 3x(x-1), because each denominator divides into it evenly - dividing it by (x-1) gives 3x, dividing it by 3x gives (x-1), and dividing it by x gives 3(x-1). Multiplying each term by 1 may seem pointless. However, there's a trick. 1 can be defined as any number over itself - 2/2 and 3/3, for example, are also valid ways of writing "1." This method takes advantage of this alternate definition. Multiply each fraction in your rational equation by 1, writing 1 each time as the number or term which multiplies with each denominator to give the LCD over itself. In our basic example, we would multiply x/3 by 2/2 to get 2x/6 and multiply 1/2 by 3/3 to get 3/6. 3x +1/6 already has 6, the LCD, as its denominator, so we can either multiply it by 1/1 or leave it alone. In our example with variables in the denominators of our fractions, the process is slightly trickier. Since our LCD is 3x(x-1), we multiply each rational expression by the term which it multiplies with to give 3x(x-1) over itself. We would multiply 5/(x-1) by (3x)/(3x) giving 5(3x)/(3x)(x-1), multiply 1/x by 3(x-1)/3(x-1) to give 3(x-1)/3x(x-1), and multiply 2/(3x) by (x-1)/(x-1) to give 2(x-1)/3x(x-1). Now that every term in your rational equation has the same denominator, you can eliminate the denominators from the equation and solve the numerators. Simply multiply both sides of the equation to get your numerators by themselves. Then, use algebraic operations to get x (or whatever other variable you are solving for) alone by itself on one side of the equals sign. In our basic example, after multiplying every term by alternate forms of 1, we get 2x/6 + 3/6 = (3x+1)/6. Two fractions can be added together if they have the same denominator, so we can simplify this equation as (2x+3)/6 = (3x+1)/6 without changing its value. Multiply both sides by 6 to cancel the denominators, which leaves us with 2x+3 = 3x+1. Subtract 1 from both sides to get 2x+2 = 3x, and subtract 2x from both sides to get 2 = x, which can be written as x = 2. In our example with variables in the denominators, our equation after multiplying each term by "1" is 5(3x)/(3x)(x-1) = 3(x-1)/3x(x-1) + 2(x-1)/3x(x-1). Multiplying each term by our LCD allows us to cancel the denominators, giving us 5(3x) = 3(x-1) + 2(x-1). This works to 15x = 3x - 3 + 2x -2, which simplifies to 15x = x - 5. Subtracting x from both sides gives 14x = -5, which, finally, simplifies to x = -5/14.
Summary: Know when finding a Lowest Common Denominator is appropriate. Examine the denominator of each fraction. Multiply each fraction, in the rational equation by 1. Simplify and solve for x.

INPUT ARTICLE: Article: You are a beautiful person just by dint of being you. Your life is a precious miracle, your individuality is special. While fashion fads, preferences for certain body shapes or parts and styling requirements come and go, one thing never changes, and that is that you matter. You can always work on attitude and appearance but never forget that your very essence is something to always be proud of. Realize that you deserve to have a healthy, happy and well educated life. You are also responsible for ensuring that this happens. Confidence is a skill that can be learned and practiced. The more you put it into practice, the more it will become second nature. If you grow up in a gregarious society, such as the United States, it's an expectation, so you'll have plenty of role models to imitate. Smiling shows that you're happy and comfortable in your own skin. Smiles suggest that you're approachable, friendly and nice to talk to. Don't just give the impression of being nice, then fail to deliver. To be seen as beautiful, it's important to exude a beautiful attitude toward everyone. That means showing other people kindness, consideration, thoughtfulness and compassion. Each of these will add up to your beautiful aura. Make the most of your natural talents by working hard to hone them. Learn as many skills as you can so that you can be self-sufficient, capable and most importantly of all, competent. You owe it to yourself to be a fully-rounded person who can do things for herself.

SUMMARY:
Appreciate what you have got already. Learn to be confident. Smile often and with authenticity. Be nice. Honor your abilities and skills.