Simplify the rational expression:

\[
\frac{x^2-49}{x^2+x-56}
\]

The choices are as follows:

A. \(\frac{x-7}{x+8}\)

B. \(\frac{x+7}{x+8}\)

C. \(\frac{x+7}{x-8}\)

D. \(\frac{x-7}{x-8}\)

for x^2-49 this is a diffarence of two perfect squares. I suggest that this is memorised. a^2-b^2=(a-b)(a+b) so x^2-7^2=(x-7)(x+7)
so to solve x^2+x-56 you want to find out what two numbers add to 1 and multiply to make -56 since -56 is negative we know that the two number are difarent signs so that eliminatess answers B and D. if we try answer C -8+7=-1 so the answer is not C because we want +1 not -1 then we see that 8+(-7)=1 so the answer is A

Answered by apologiabiology | 2024-06-10

You want to use the reverse FOIL method to break up the equation. (front, outer, inner, last) When you do this, you can simplify the equation down to (x+8)*(x-7). That is equivalent to x^2+8x-7x-56 or x^2+x-56.

Answered by Stude707 | 2024-06-10

The simplified form of the rational expression x 2 + x − 56 x 2 − 49 ​ is x + 8 x + 7 ​ . Therefore, the correct answer is option B. This is achieved by factoring both the numerator and the denominator and canceling the common factor.
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Answered by apologiabiology | 2024-12-26