Question

Resolva a equação
$\frac{10}{x} + \frac{16}{x - 1} = \frac{30}{x}$
​

Answer 1

$\frac{10}{x}+\frac{16}{x-1}=\frac{30}{x}\\\\\frac{10.[x(x-1)]}{x}+\frac{16.[x(x-1)]}{x-1}=\frac{30.[x(x-1)]}{x}\\\\10(x-1)+16x=30(x-1)\\\\10x-10+16x=30x-30\\\\26x-10=30x-30\\\\26x-10+30-26x=30x-30+30-26x\\\\20=4x\\\\\frac{20}{4}=\frac{4x}{4}\\\\x=5$

Answer 2

$\displaystyle \frac{10}{\text x}+\frac{16}{\text x-1}=\frac{30}{\text x}$

1º vamos achar as restrições.

não podemos ter 0 no numerador, logo :

$\boxed{\text x \neq 0} \\\\ \text x -1\neq 0 \to \boxed{\text x\neq 1}$

Agora vamos pegar a equação e tirar o MMC :

$\displaystyle \frac{10}{\text x/(\text x-1)}+\frac{16}{(\text x-1)/\text x}=\frac{30}{\text x} \\\\\\ \frac{10(\text x-1)}{\text x(\text x-1)} + \frac{16\text x}{\text x(\text x-1)} = \frac{30}{\text x} \\\\\\ \frac{10\text x-10+16\text x}{\text x(\text x-1)} = \frac{30}{\text x} \\\\\\ 26\text x-10 = \frac{30\text x(\text x-1) }{\text x} \\\\\\ 26\text x-10 = 30(\text x-1) \\\\ \text 26\text x-10 =30\text x -30 \\\\ 30\text x -26\text x = 30 -10 \\\\ 4\text x =20 \\\\ \underline{\text{portanto :}}$

$\huge\boxed{\text x=5} \checkmark$