Question

practice: solve rational equations
score: 3/6 answered: 3/6
question 4
solve the equation \\(\frac{7x + 8}{x + 9} = \frac{57}{x + 9}\\)
\\(x = \\) (if needed, enter your answer as a reduced fraction.)

Explanation:

Step1: Eliminate the denominator

Since the denominators \(x + 9\) are the same (and \(x
eq - 9\) to avoid division by zero), we can multiply both sides of the equation \(\frac{7x + 8}{x + 9}=\frac{57}{x + 9}\) by \(x + 9\) to get \(7x+8 = 57\).

Step2: Solve for \(x\)

Subtract 8 from both sides: \(7x=57 - 8\), so \(7x = 49\). Then divide both sides by 7: \(x=\frac{49}{7}=7\). We check that \(x = 7\) does not make the denominator zero (\(7+9=16
eq0\)), so it is a valid solution.

Answer:

\(x = 7\)