Question

Find for x
3/x+1+4/x-1=29/4x-1; x=not 1, -1, 1/4​

Answer 1

$\bf \underline{Question} \\ \bf Solve\ for\ x\\ \rm \frac{3}{x+1}+\frac{4}{x-1}=\frac{29}{4x-1}; x\neq 1, -1 and\ \frac{1}{4}$

$\bf \underline{Answer}\\ \bf x=4\ and\ -7$

Step-by-step explanation:

Given, equation is

$\rm \frac{3}{x+1}+\frac{4}{x-1}=\frac{29}{4x-1}\\ \\ \\ \implies \rm \frac{3(x-1)+4(x+1)}{x^2-1}=\frac{29}{4x-1}\qquad \qquad \{\because (a+b)(a-b)=a^2-b^2\}\\ \\ \\ \implies \rm \frac{3x-3+4x+4}{x^2-1}=\frac{29}{4x-1}\\ \\ \\ \implies \rm \frac{7x+1}{x^2-1}=\frac{29}{4x-1}\\ \\ \\ \implies \rm (7x+1) (4x-1)=29 (x^2-1)\qquad \qquad \{Cross-multiplication\}\\ \\ \implies \rm 28x^2-7x+4x-1=29x^2-29\\ \\ \implies \rm 28x^2-3x-1=29x^2-29\\ \\ \implies \rm x^2=28-3x\\ \\ \implies \rm x^2+3x-28=0\\ \\ \implies \rm x^2+7x-4x-28=0\\ \\ \implies \rm x(x+7) -4(x+7)=0\\ \\ \implies \rm (x-4) (x+7)=0\\ \\ \bf \therefore x=4\ and\ -7$