Question

question 5 of 10, step 1 of 1 solve the following rational equation and simplify your answer. \\(\frac{8x}{x - 2} = \frac{7x}{x - 1}\\) answer separate multiple answers with commas. \\(x = \\)

Explanation:

Step1: Cross-multiply to eliminate denominators

$8x(x-1) = 7x(x-2)$

Step2: Expand both sides

$8x^2 - 8x = 7x^2 - 14x$

Step3: Move all terms to left side

$8x^2 - 8x -7x^2 +14x = 0$

Step4: Simplify the quadratic expression

$x^2 +6x = 0$

Step5: Factor out common term

$x(x+6) = 0$

Step6: Solve for x, check domain

$x=0$ or $x=-6$; verify $x
eq1,2$, both are valid.

Answer:

$x = 0, -6$