Question

x² - 1/x + 1 = 4

x = ?

Answer 1

Given equation,

$\frac{x^{2}-1 }{x+1} =4$

This can be solved as,

$x^{2} -1=4(x+1)$

$x^{2} -1=4x+4$

$x^{2} -4x-5=0$

$x^{2} -5x+x-5=0$

$x(x-5)+1(x-5)=0$

$(x-5)(x+1)=0$

$x-5=0,x+1=0\\x=5,x=-1$

Therefore the value of $x$ is $5,-1$.

Answer 2

Given,

$\frac{x^{2}-1}{x+1}=4$

From the formula,

$a^{2}-b^{2}=(a+b)(a-b)$

Numerator $x^{2} -1$ can be written as $(x-1)(x+1)$

So,

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

$x-1=4\\x=5$

Therefore, the value of $x$ is $5$.