Question

What is the common denominator of 5/x^2-4 - 2/x+2 in the complex fraction 2/x-2 - 3/x^2-4 divided by 5/x^2-4 - 2/x+2

A) (x + 2)(x - 2)

B) x - 2

C) (x + 2)^2(x - 2)

D) x + 2

Answer 1

A) (x + 2)(x - 2)

Explanation:

truth me

Answer 2

Answer: A) (x + 2)(x - 2)

Explanation:

The given complex fraction is

`\Rightarrow((2)/((x-2))-(3)/(x^2-4) )/((5)/((x^2-4))-(2)/(x+2))\\\\\text{Using identity, }a^2-b^2=(a+b)(a-b)\\\\\Rightarrow((2)/((x-2))-(3)/((x-2)(x+2)))/((5)/((x-2)(x+2))-(2)/(x+2))\\\\\text{Taking LCM, we get}\\\\\Rightarrow ((2(x+2)-3)/((x-2)(x+2)\leftarrow same ))/((5-2(x-2))/((x+2)(x-2)\leftarrow same))`

Thus we can see that the common denominator in the above complex fraction is A) (x + 2)(x - 2)