Question

Solve for x :1/(x+1)+2/(x+2)=4/x+4, x not= -1,-2,-4.

Answer 1

1/(x+1) + 2 /(x+2) = 4/(x+4)

[(x+2) + 2(x+1)]/(x+1)(x+2) = 4/(x+4)

(x+2+2x+2)/(x+1)(x+2) = 4/(x+4)

(3x+4)(x+4) = 4(x+1)(x+2)

3x^2 + 4x+12x +16 = 4(x^2 + 3x+2)

3x^2+16x+16 = 4x^2+12x + 8

16x-12x+16-8 = 4x^2

4x+8=4x^2

x+2=x^2

=>> x^2-x-2

=>> x^2+x-2x-2

=>> x(x+1)-2(x+1)

=>> (x-2)(x+1) = 0

=>> x = 2,-1