Question

Solve the rational equation 8/x+1/5=3/x

Answer 1

We are going to solve the rational equation $\frac{8}{x+ \frac{1}{5} } = \frac{3}{x}$

Step 1. Simplify the denominator of the left hand side of the equation:
$\frac{8}{x+ \frac{1}{5} } = \frac{3}{x}$
$\frac{8}{ \frac{5x+1}{5} } = \frac{3}{x}$
$\frac{40}{5x+1} = \frac{3}{x}$

Step 2. Multiply both sides of the equation by $(5x+1)$ and $x$:
$\frac{40}{5x+1}(5x+1)(x) = \frac{3}{x}(5x+1)(x)$
$40x=3(5x+1)$
$40x=15x+3$

Step 3. Subtract $15x$ from both sides of the equation:
$40x-15x=15x-15x+3$
$25x=3$

Step 4. Divide both sides of the equation by 25:
$\frac{25x}{25} = \frac{3}{25}$
$x= \frac{3}{25}$

We can conclude that the solution of the rational equation is $x= \frac{3}{25}$