Question

Subtract: 4x/x^2-25 - 2/x^2+2x-15

a. 4x^2-14x+10/(x+5)(x-3)
b. 4x^2-14x-10/(x-5)(x+5)(x-3)
c. 4x^2-14x-10/(x-5)^2(x-3)
d. 4x^2-14x-10/(x-5)(x+5)(x-3)

Answer 1

Answer:
`(4x^2-14x+10)/((x-5)(x+5)(x-3))`

Explanation:

Given

Subtract the expression

`\Rightarrow (4x)/(x^2-25)-(2)/(x^2+2x-15)\\\\\Rightarrow (4x)/((x-5)(x+5))-(2)/(x^2+5x-3x-15)\\\\\Rightarrow (4x)/((x-5)(x+5))-(2)/((x+5)(x-3))\\\\\text{Take the LCM and subtract}\\\\\Rightarrow (4x(x-3)-2(x-5))/((x-5)(x+5)(x-3))\\\\\Rightarrow (4x^2-12x-2x+10)/((x-5)(x+5)(x-3))\\\\\Rightarrow (4x^2-14x+10)/((x-5)(x+5)(x-3))`