Question

Qual é a fração algébrica que, somada à fração x+1/2x-4. da como o resultado 5x+1/3x-6 ?

Answer 1

$\mathrm{\dfrac{x+1}{2x-4}+y=\dfrac{5x+1}{3x-6}\ \to\ y=\dfrac{5x+1}{3(x-2)}-\dfrac{x+1}{2(x-2)}}\\\\\\ \mathrm{y=\dfrac{(5x+1).2(x-2)-(x+1).3(x-2)}{3(x-2).2(x-2)}}\\\\\\ \mathrm{y=\dfrac{(x-2)[2(5x+1)-3(x+1)]}{6(x-2)^2}=\dfrac{10x+2-3x-3}{6(x-2)}}\\\\\\ \boxed{\mathbf{y=\dfrac{7x-1}{6x-12}}}$