Question

dilation & scale factor hw (word problems)
solve for x
\\(\frac{x}{x - 3} = \frac{x + 1}{x - 4}\\)
\\(x = \square\\)

Explanation:

Step1: Cross-multiply to eliminate fractions

$x(x-4) = (x+1)(x-3)$

Step2: Expand both sides

$x^2 - 4x = x^2 - 3x + x - 3$

Step3: Simplify right-hand side

$x^2 - 4x = x^2 - 2x - 3$

Step4: Subtract $x^2$ from both sides

$-4x = -2x - 3$

Step5: Isolate x terms

$-4x + 2x = -3$

Step6: Solve for x

$-2x = -3 \implies x = \frac{3}{2}$

Answer:

$\frac{3}{2}$