Everyday Math

# Componendo and Dividendo

If $\displaystyle \frac{a}{b} = \frac{3}{14},$ what is $\displaystyle \frac{b-a}{b+a}?$

If $\displaystyle \frac{x^2+8x-9}{x^2-8x-9} = \frac{x+9}{x-9},$ what is $x?$

If $\frac{a-b}{a+b} = \frac{ 3} { 8 }$, then find the value of

$\frac{ 5a + 3b } { 5a - 3b }.$

If $\displaystyle \frac{\sqrt{7}+x}{\sqrt{7}-x} = 7,$ what is $x?$

If $\displaystyle \frac{20+x}{20-x} = 4,$ what is $x?$

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