Question

solve for x and simplify the answer fully.
$\frac{5}{x-3}=\frac{7}{x-9}$

Explanation:

Step1: Cross-multiply to eliminate denominators

$5(x - 9) = 7(x - 3)$

Step2: Expand both sides of the equation

$5x - 45 = 7x - 21$

Step3: Rearrange terms to isolate x

$5x - 7x = 45 - 21$

Step4: Simplify and solve for x

$-2x = 24$
$x = \frac{24}{-2}$

Answer:

$x = -12$