Will Give Medal for best answer and help c:
( ALGEBRA 2)
I have to figure out the errors the did while solving :
Two fellow students, Theo and Paula, have added two rational expressions. They ended up with different answers, so they have asked you to check their work. Please explain to them any errors that you find.
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Theo's mistake is in the second step where he multiplied the top of the expression on the left by (x+2). First of all it is not necessary to do that multiplication because the expression at the bottom (x-5)(x+2) is already the common denominator and therefore there is no need to multiply this expression by any factor. Secondly, any time you multiply the top you should also multiply the bottom to preserve the ratio. Theo only multiplies the top and not the bottom and therefore he has altered the ratio.
Paula's mistake is in the fourth step where she factors x^2-4x-5 into (x+2)(x-5) which is wrong factoring. Also, factoring is not needed here. Since the denominators of the two expressions is the same the numerator can be added. The mistake continues in the next step where she cancels out factors across an addition. You cannot do that. There is a plus sign between the two expressions and common factors cannot be cancelled out across addition or subtraction.