R K Bansal Solutions for Exercise 1: EXERCISE

If $x=\frac{6ab}{a+b},$ find the value of : $\frac{x+3a}{x-3a}+\frac{x+3b}{x-3b}.$

If $\frac{x^2+y^2}{x^2-y^2}=2\frac{1}{8},$ find $\frac{x^3+y^3}{x^3-y^3}$.

Using componendo and dividendo, find the value of $x$ : $\frac{\sqrt{3x+4}+\sqrt{3x+5}}{\sqrt{3x+4}-\sqrt{3x-5}}=9.$

Given $\frac{x^3+12x}{6x^2+8}=\frac{y^3+27y}{9y^2+27}$. Using componendo and dividendo, find $x : y.$

If $\frac{7m+2n}{7m-2n}=\frac{5}{3}$ use properties of proportion to find$m : n$.

If $\frac{7m+2n}{7m-2n}=\frac{5}{3}$, use properties of proportion to find$\frac{m^2+n^2}{m^2-n^2}$.

If $x$ and $y$ both are positive and $(2x^2-5y^2) : xy= 1:3$, find $x : y$.

Find $x,$ if $16{\left(\frac{a-x}{a+x}\right)}^3=\frac{a+x}{a-x}.$