Question

Write a rational expression with denominator (x - 3)(x + 2) that is equivalent to 3x-1/x+2

Answer 1

(x-3)(3x-1)/((x-3)(x+2))

Explanation:

An equivalent fraction is formed by multiplying or dividing numerator and denominator by the same factor.

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To get the desired denominator, the given denominator must be multiplied by (x-3). To get the desired numerator of the equivalent fraction, the numerator must also be multiplied by (x-3).

`(3x-1)/(x+2)=\boxed{((x-3)(3x-1))/((x-3)(x+2))=(3x^2-10x+3)/(x^2-x-6)}`