High School

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simplify into one fraction
7/x-3 + 3/x-5

simplify into one fraction
-5/x-3 - -4.x+2

simplify into one fraction
6/x+7 - 3/x-2

Answer :

To simplify the given expressions into one fraction, we find a common denominator for each set of fractions, adjust the numerators accordingly, and then combine the numerators over the common denominator.

To simplify the given expressions into one fraction, we need to find a common denominator and combine the fractions accordingly. Let's go through each expression step by step.

For the expression 7/x-3 + 3/x-5, the common denominator would be (x-3)(x-5). We need to multiply each fraction by the denominator that it's missing to get common denominators, and then sum the numerators over the common denominator.

The expression -5/x-3 - (-4)/(x+2) involves subtracting fractions. To simplify, we again find a common denominator, which is (x-3)(x+2), and proceed similarly to the first expression.

For 6/x+7 - 3/x-2, the common denominator is (x+7)(x-2). We perform the same process of equating denominators and combining.

To illustrate with the first expression:
(7(x-5))/((x-3)(x-5)) + (3(x-3))/((x-3)(x-5)) = (7x - 35 + 3x - 9)/((x-3)(x-5))

Combine the numerators to get a single fraction:

(10x - 44)/((x-3)(x-5))

Apply the same approach to the other two expressions to get them into a single fraction form.

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Rewritten by : Barada