PSAT Math : How to find the solution of a rational equation with a binomial denominator

Study concepts, example questions & explanations for PSAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #2 : Binomials

Solve for \(\displaystyle x\).

\(\displaystyle \frac{x^{2}+2x-8}{x^{2}+5x-14}=\frac{3}{4}\)

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle 0\)

\(\displaystyle 3\)

\(\displaystyle 5\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 5\)

Explanation:

\(\displaystyle \frac{x^{2}+2x-8}{x^{2}+5x-14}=\frac{3}{4}\)

Factor the expression

numerator: find two numbers that add to 2 and multiply to -8 [use 4,-2]

denominator: find two numbers that add to 5 and multiply to -14 [use 7,-2]

 

new expression:

\(\displaystyle \frac{(x+4)(x-2)}{(x+7)(x-2)}=\frac{3}{4}\)

Cancel the \(\displaystyle x-2\) and cross multiply.

\(\displaystyle 4(x+4)=3(x+7)\)

\(\displaystyle 4x+16=3x+21\)

\(\displaystyle x=5\)

Learning Tools by Varsity Tutors