Question

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$\frac{3}{x - 5}=\frac{3}{7}$ has solutions $x = 12$
$\frac{3}{x - 5}=\frac{3}{x + 5}$ has solutions $x = none$
$\frac{3}{x - 5}=\frac{3}{2x+5}$ has solutions $x=-10$
$\frac{3}{x - 5}=\frac{2}{x - 5}$ has solutions $x = none$
$\frac{2}{x - 5}=\frac{3}{x + 5}$ has solutions $x = 25$
$\frac{16}{x - 9}=\frac{6}{x + 29}$ has solutions $x=-81.6$

Explanation:

Step1: Cross - multiply the equation $\frac{16}{x - 9}=\frac{6}{x + 29}$

$16(x + 29)=6(x - 9)$

Step2: Expand both sides

$16x+464 = 6x-54$

Step3: Move the $x$ terms to one side and constants to the other

$16x - 6x=-54 - 464$

Step4: Simplify both sides

$10x=-518$

Step5: Solve for $x$

$x = - 51.8$

Answer:

$x=-51.8$