Question

Se de uma fração A subtrairmos a fração a-x/a+1, vamos obter 2a(x+1) / a^2-1. Nessas condisoes qual é a fração A?

Answer 1

$A-\dfrac{a-x}{a+1}=\dfrac{2a\left(x+1\right)}{a^{2}-1}\Rightarrow A=\dfrac{2a\left(x+1\right)}{a^{2}-1}+\dfrac{a-x}{a+1}\Rightarrow\\ \\ \\ A=\dfrac{2ax+2a}{\left(a+1\right)\left(a-1\right)}+\dfrac{a-x}{a+1}\Rightarrow A=\dfrac{2ax+2a+\left(a-x\right)\left(a-1\right)}{\left(a+1\right)\left(a-1\right)}\\ \\ \\ A=\dfrac{2ax+2a+a^{2}-a-ax+x}{\left(a+1\right)\left(a-1\right)}\Rightarrow A=\dfrac{ax+a+a^{2}+x}{\left(a+1\right)\left(a-1\right)}\Rightarrow$


$A=\dfrac{ax+a+a^{2}+x}{\left(a+1\right)\left(a-1\right)}\Rightarrow A=\dfrac{ax+x+a+a^{2}}{\left(a+1\right)\left(a-1\right)}\Rightarrow\\ \\ \\ A=\dfrac{x\left(a+1\right)+a\left(a+1\right)}{\left(a+1\right)\left(a-1\right)}\Rightarrow A=\dfrac{\left(a+1\right)\left(x+a\right)}{\left(a+1\right)\left(a-1\right)}\Rightarrow A=\dfrac{x+a}{a-1}$