Question

5/a-2 + 3a-14/a²-4 - 5/a+2=

Answer 1

A expressão é:

$\mathsf{\dfrac{5}{a-2}+\dfrac{3a-14}{a^2-4}-\dfrac{5}{a+2}}$

Lembrando da propriedade:

$\mathsf{\left(a+b\right)\cdot \left(a-b\right)=a^2-b^2}$

Assim, podemos reescrever:

$\mathsf{a^2-4=\left(a-2\right)\cdot \left(a+2\right)}$

Substituindo na expressão:

$\mathsf{\dfrac{5}{a-2}+\dfrac{3a-14}{\left(a+2\right)\cdot \left(a-2\right)}-\dfrac{5}{a+2}}\\\\\\\mathsf{\dfrac{5\cdot \left(a+2\right)}{\left(a-2\right)\cdot \left(a+2\right)}+\dfrac{3a-14}{\left(a+2\right)\cdot \left(a-2\right)}-\dfrac{5\cdot \left(a-2\right)}{\left(a+2\right)\cdot \left(a-2\right)}}\\\\\\\mathsf{\dfrac{5\left(a+2\right)+\left(3a-14\right)-5\left(a-2\right)}{\left(a-2\right)\cdot \left(a+2\right)}}\\\\\\\mathsf{\dfrac{5a+10+3a-14-5a+10}{\left(a-2\right)\cdot \left(a+2\right)}}$
$\\\\\\\mathsf{\dfrac{3a+6}{\left(a-2\right)\cdot \left(a+2\right)}}\\\\\\\mathsf{\dfrac{3\cdot \left(a+2\right)}{\left(a-2\right)\cdot \left(a+2\right)}}\\\\\\\boxed{\boxed{\mathsf{\dfrac{3}{\left(a-2\right)}}}}$