Question

Solve the following equation : 1/x+1 +2/x+2= 1/ x+5, x is not equal to -1,-2,-4

Answer 1

Answer:

Explanation:

Given:-

$\frac{1}{x+1}+\frac{2}{x+2}=\frac{1}{x+5}$

To Find:-

x

Solution:-

$\frac{1}{x+1}+\frac{2}{x+2}=\frac{1}{x+5}$

Taking LCM on LHS:-

$\frac{1(x+2)+2(x+1)}{(x+1)(x+2)}=\frac{1}{x+5}$

$\frac{x+2+2x+2}{x^2+2x+x+2}=\frac{1}{x+5}$

$\frac{3x+4}{x^2+3x+2}=\frac{1}{x+5}$

Cross Multiplying Both Side:-

(3x+4)(x+5)=x²+3x+2

3x²+15x+4x+20=x²+3x+2

3x²-x²+19x-3x+20-2=0

2x²+16x+18=0

2(x²+8x+9)=0

x²+8x+9=0

This Quadratic Equation is solved in the attachment...

Hope it helps you...