Question

Solve for x. 4/x−3+2/x^2−9=1/x+3

Answer 1

`x=-(17)/(3)`

Explanation:

we have

`(4)/(x-3)+(2)/(x^(2)-9)=(1)/(x+3)`

Solve for x

Applying difference of squares in the denominator of the second term in the left side

`(4)/(x-3)+(2)/((x+3)(x-3))=(1)/(x+3)`

Multiply both sides by (x+3)(x-3)

`4(x+3)+2=(x-3)`

Apply the distributive property in the left side

`4x+12+2=x-3`

Combine like terms left side

`4x+14=x-3`

Group terms

`4x-x=-3-14`

`3x=-17`

Divide by 3 both sides

`x=-(17)/(3)`