Componendo and Dividendo

         

If ab=314,\displaystyle \frac{a}{b} = \frac{3}{14}, what is bab+a?\displaystyle \frac{b-a}{b+a}?

If x2+8x9x28x9=x+9x9,\displaystyle \frac{x^2+8x-9}{x^2-8x-9} = \frac{x+9}{x-9}, what is x?x?

If aba+b=38 \frac{a-b}{a+b} = \frac{ 3} { 8 } , then find the value of

5a+3b5a3b. \frac{ 5a + 3b } { 5a - 3b }.

If 7+x7x=7,\displaystyle \frac{\sqrt{7}+x}{\sqrt{7}-x} = 7, what is x?x?

If 20+x20x=4,\displaystyle \frac{20+x}{20-x} = 4, what is x?x?

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