Question

solve the equation X square + 1 is equal to a upon A + B Into X + A + B Upon A Into X​

Answer 1

Answer:

Solution

$x=\frac{a+b}{a},\frac{a}{a+b}$

Step-by-step explanation:

Given:

$x^2+1=\frac{a}{a+b}x+\frac{(a+b)}{a}x$

$\implies\:x^2+1=x[\frac{a}{a+b}+\frac{(a+b)}{a}]$

$\implies\:x^2+1=x[\frac{a^2+(a+b)^2}{a(a+b)}]$

$\implies\:(x^2+1)a(a+b)=x(a^2+(a+b)^2)$

$\implies\:a(a+b)x^2+a(a+b)=x(a^2+(a+b)^2)$

$\implies\:a(a+b)x^2-x(a^2+(a+b)^2)++a(a+b)=0$

$\implies\:a(a+b)x^2-a^2x-(a+b)^2x+a(a+b)=0$

$\implies\:ax((a+b)x-a)-(a+b)((a+b)x-a)=0$

$\implies\:(ax-(a+b))((a+b)x-a)=0$

$\implies\:ax-(a+b)=0\:or\:(a+b)x-a=0$

$\implies\:ax=a+b\:or\:(a+b)x=a$

$\implies\:\boxed{x=\frac{a+b}{a},\frac{a}{a+b}}$