Solve for x: 2 over quantity x minus 2 plus 7 over quantity x squared minus 4 equals 5 over x.

Mathematics

2 answers:

Iteru [2.4K]4 years ago

8 0

Answer: The correct option is

(B) $x=-\dfrac{4}{3},~~5.$

Step-by-step explanation: We are given to solve the following equation for x :

"2 over quantity x minus 2 plus 7 over quantity x squared minus 4 equals 5 over x."

The above equation can be written as :

$\dfrac{2}{x-2}+\dfrac{7}{x^2-4}=\dfrac{5}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following formula to solve equation (i) :

$a^2-b^2=(a+b)(a-b).$

The solution of equation (i) is as follows :

$\dfrac{2}{x-2}+\dfrac{7}{x^2-4}=\dfrac{5}{x}\\\\\\\Rightarrow \dfrac{2}{x-2}+\dfrac{7}{(x+2)(x-2)}=\dfrac{5}{x}\\\\\\\Rightarrow \dfrac{2(x+2)+7}{(x+2)(x-2)}=\dfrac{5}{x}\\\\\\\Rightarrow \dfrac{2x+11}{x^2-4}=\dfrac{5}{x}\\\\\Rightarrow 2x^2+11x=5x^2-20\\\\\Rightarrow 5x^2-2x^2-11x-20=0\\\\\Rightarrow 3x^2-11x-20=0\\\\\Rightarrow 3x^2-15x+4x-20=0\\\\\Rightarrow 3x(x-5)+4(x-5)=0\\\\\Rightarrow (3x+4)(x-5)=0\\\\\Rightarrow 3x+4=0,~~~x-5=0\\\\\Rightarrow x=-\dfrac{4}{3},~5.$