Question

solve x :1/ x+1+3/5x+1=5/x+4 where x is not equal to -1,-1/5,-4
Plzzz solve it fast.....!!!

Answer 1

Answer:

Step-by-step explanation:

It is short...

I hope it helps........

Answer 2

Answer:

$x = 1 \:Or\: x = \frac{-11}{17}$

Explanation:

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

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

$\implies \frac{8x+4}{5x^{2}+x+5x+1}=\frac{5}{x+4}$

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

Do the cross multiplication,we get

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

$\implies (8x^{2}+32x+4x+16)=25x^{2}+30x+5$

$\implies (8x^{2}+36x+16)=25x^{2}+30x+5$

$\implies 0=25x^{2}+30x+5-8x^{2}-36x-16$

$\implies 17x^{2}-6x-11=0$

Splitting the middle term, we get

$\implies17x^{2}-17x+11x-11=0$

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

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

$\implies x-1 = 0\: Or \: 17x+11=0$

$\implies x = 1 \:Or\: x = \frac{-11}{17}$

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