Question

Factorise the given equation X + 1 upon x minus 1 minus x minus one upon X + 1 equals to 5 by 6

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{5}{6}}$

$\underline{\textsf{To find:}}$

$\textsf{Factors of}$

$\mathsf{\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{5}{6}}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{5}{6}}$

$\mathsf{\dfrac{(x+1)^2-(x-1)^2}{(x-1)(x+1)}=\dfrac{5}{6}}$

$\mathsf{\dfrac{(x+1)^2-(x-1)^2}{x^2-1}=\dfrac{5}{6}}$

$\mathsf{\dfrac{(x^2+1+2x)-(x^2+1-2x)}{x^2-1}=\dfrac{5}{6}}$

$\mathsf{\dfrac{4x}{x^2-1}=\dfrac{5}{6}}$

$\mathsf{6(4x)=5(x^2-1)}$

$\mathsf{24x=5x^2-5}$

$\mathsf{5x^2-24x-5=0}$

$\mathsf{5x^2-25x+x-5=0}$

$\mathsf{5x(x-5)+1(x-5)=0}$

$\mathsf{(5x+1)(x-5)=0}$

$\implies\boxed{\mathsf{x=5,\dfrac{-1}{5}}}$

$\underline{\textsf{Answer:}}$

$\textsf{The factors are (5x+1) and (x-5)}$

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Answer 2

Answer:

x=5,-1/5

Step-by-step explanation:

see the attachment