Question

Solve for x. 4/x−3+2/x^2−9=1/x+3

Answer 1

Answer:

$x=-\frac{17}{3}$

Step-by-step explanation:

we have

$\frac{4}{x-3}+\frac{2}{x^{2}-9}=\frac{1}{x+3}$

Solve for x

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

$\frac{4}{x-3}+\frac{2}{(x+3)(x-3)}=\frac{1}{x+3}$

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

$x=-\frac{17}{3}$