Question

Solve x :1/ x+1+3/5x+1=5/x+4

Answer 1

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Answer 2

Answer:

$x=1,x=\frac{-11}{17}$    

Step-by-step explanation:

Given :  $\frac{1}{x+1}+\frac{3}{5x+1}=\frac{5}{x+4}$.......[1]

Solve : Equation [1]

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

Taking LCM

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

$\frac{5x+1+3x+3)}{(5x^2+6x+1)}=\frac{5}{x+4}$

$\frac{8x+4}{(5x^2+6x+1)}=\frac{5}{x+4}$

Cross multiply

$(8x+4)\times(x+4)=(5x^2+6x+1)\times 5$

$(8x^2+32x+4x+16)=(25x^2+30x+5)$

$8x^2+36x+16=25x^2+30x+5$

$8x^2-25x^2+36x-30x+16-5=0$

$-17x^2+6x+11=0$

$17x^2-6x-11=0$

$17x^2-17x+11x-11=0$ (Middle term split)

$(x-1)(17x+11)=0$

x=1 , $x=\frac{-11}{17}$