INPUT ARTICLE: Article: The following terms will be used throughout the examples, and are common in problems involving algebraic fractions: Numerator: The top part of a fraction (ie. (x+5)/(2x+3)). Denominator: The bottom part of the fraction (ie. (x+5)/(2x+3)). Common Denominator: This is a number that you can divide out of both the top and bottom of a fraction. For example, in the fraction 3/9, the common denominator is 3, since both numbers can be divided by 3. Factor: One number that multiples to make another. For example, the factors of 15 are 1, 3, 5, and 15. The factors of 4 are 1, 2, and 4. Simplified Equation: This involves removing all common factors and grouping similar variables together (5x + x = 6x) until you have the most basic form of a fraction, equation, or problem. If you cannot do anything more to the fraction, it is simplified. These are the exact same steps you will take to solve algebraic fractions. Take the example, 15/35. In order to simplify a fraction, we need to find a common denominator. In this case, both numbers can be divided by five, so you can remove the 5 from the fraction: 15 5 * 335 5 * 7 Now you can cross out like terms. In this case you can cross out the two fives, leaving your simplified answer, 3/7. In the previous example, you could easily remove the 5 from 15, and the same principle applies to more complex expressions like, 15x 5. Find a factor that both numbers have in common. Here, the answer is 5, since you can divide both 15x and -5 by the number five. Like before, remove the common factor and multiply it by what is "left."15x 5 = 5 * (3x 1) To check your work, simply multiply the five back into the new expression you will end up with the same numbers you started with. The same principle used in common fractions works for algebraic ones as well. This is the easiest way to simplify fractions while you work. Take the fraction: (x+2)(x-3)(x+2)(x+10) Notice how the term (x+2) is common in both the numerator (top) and denominator (bottom). As such, you can remove it to simplify the algebraic fraction, just like you removed the 5 from 15/35: (x+2)(x-3) (x-3)(x+2)(x+10) (x+10) This leaves us with our final answer: (x-3)/(x+10)

SUMMARY: Know the vocabulary for algebraic fractions. Review how to solve simple fractions. Remove factors from algebraic expressions just like normal numbers. Know you can remove complex terms just like simple ones.

INPUT ARTICLE: Article: The UN states that disabled children have a right to preservation of identity, i.e., to be themselves even if it means looking autistic. Research has shown that autistic people who attempt to "camouflage" their autism are at significantly higher risk of suicide. A good therapist will value the person's individuality and mental health by allowing and encouraging them to be different. They should not try to remove autistic behaviors or characteristics like... Most stimming (You may hear phrases such as "quiet hands" and "table ready" to indicate suppression of stims.) Toe-walking Avoidance of eye contact Introversion or a desire for a quiet social life Other quirks (Fitting in should be a personal choice, not forced by others.) Some therapists train autistic people to show facial expressions or body language that suggest happiness, regardless of their actual feelings. All people need to be able to express their feelings. No one should be pushed to smile or act happy if they do not feel happy. Dog trainers consider dogs that have been trained not to growl or show aggression as "time bomb dogs" that are likely to attack seemingly "out of nowhere." This is because stopping a dog from acting out will not stop the fear and anxiety that caused the dog to act this way. Similarly, training a child to bottle up their distress is likely to turn them into a "time bomb" of anxiety and aggression. It may make their meltdowns more intense and unpredictable. Children should not be treated worse than dogs. Hugs and kisses should not be trained or pressured, even if it means hurting feelings. The right to set boundaries is important in arming your loved one against sexual and emotional abuse. A bad therapist may try in vain to make your loved one not be autistic; a good one will seek to work with them so they can grow into a happy and capable autistic adult. Therapists should focus on helping the person become a happy autistic person, not a non-autistic one. Good therapy goals might include... Building emotion regulation skills Finding comfortable and non-harmful stims, instead of extinguishing all stimming Finding ways to accommodate and alleviate sensory issues Gaining social skills in a friendly environment; these include assertiveness as well as making friends Discussing and working on your loved one's own personal goals Communication should be considered more important than verbal speech (including both behavior and AAC). Beginning vocabulary should focus on basic needs instead of parents' feelings. Words such as "yes," "no," "stop," "hungry," and "hurt" are more necessary than "I love you" or "Mommy." Behavior should be respected, even as someone is learning to communicate via AAC or speech.

SUMMARY: Ask yourself whether the goals involve accommodation or assimilation. Consider if the therapist controls your loved one's affect. Consider whether the therapist is fighting or accommodating the autistic person's brain. Evaluate whether learning communication is treated as an essential skill, or a performance to please adults.

INPUT ARTICLE: Article: When your nose runs, it may be due to sickness (which will likely be accompanied by other symptoms of a "cold," such as sore throat, cough, etc), being upset (when we cry, excess water from our tears drains through the nose), or cold weather (as our nasal passages are designed to heat the air before it reaches our lungs, and in order to do so your nose produces extra fluid in the cold weather). It may also be related to allergies, irritants in your environment (such as smoke), or a side effect of certain medications. When you breathe through your nose, your sinuses warm and moisten the air by swirling it around the mucous membranes that line the passages. This prevents you from irritating your lungs and throat with air that is cooler than your body temperature. Water is a by-product of this process and the excess runs down the back of your throat and out your nose. Your sinuses perform this function year round, but because of the temperature difference in cooler weather (especially in wintertime) it is more pronounced in the cold. Therefore, they are nothing to get overly worried about. They are so common, in fact, that sometimes it is called "skier's nose" due to the fact that nearly 100% of competitive snow sport athletes complain about runny nose! A runny nose from the cold is NOT related to an illness (and not related to the "common cold.") Although many people believe there is a link between cold weather and "catching a cold," this is thought to be due to spending more time indoors where people's germs are more readily passed to one another (and is not thought to be related so much to the cold outside).

SUMMARY:
Be aware of possible diagnoses. Understand why your nose runs when it's cold. Know that runny noses from the cold are extremely common.