Question

Solve for x :

${\displaystyle \frac{1}{x+1}+\frac{3}{5x+1}=\frac{5}{x+4},x\ne -1,-\frac{1}{5},-4}$

Answer 1

${\displaystyle \frac{1}{x+1}+\frac{3}{5x+1}=\frac{5}{x+4},x\ne -1,-\frac{1}{5},-4}$

 

${\displaystyle \Rightarrow \frac{5x+1+3x+3}{(x+1)(5x+1)}=\frac{5}{x+4}}$

⇒(8x + 4)(x + 4) =5(x + 1)(5x + 1)

⇒8x² + 32x + 4x + 16 = 5(5x² +x + 5x +1)

⇒8x² +36x +16 =25x² +30x +5

⇒17x² −6x −11 =0

⇒17x² − 17x + 11x − 11 = 0

⇒17x(x − 1) + 11(x − 1) = 0

⇒(17x + 11)(x − 1) = 0

⇒17x + 11 = 0 or x − 1 = 0

${\displaystyle \Rightarrow x=\frac{-11}{17}\text{or}x=1}$