If $\frac{15a^2+4b^2}{15a^2-4b^2}=\frac{47}{7}$, find the value of the ratio $\frac{7a-3b}{7a+3b}$.

If $\frac{15a^2+4b^2}{15a^2-4b^2}=\frac{47}{7}$, find the value of the ratio $\frac{b^2-2a^2}{b^2+2a^2}$.

If $\frac{15a^2+4b^2}{15a^2-4b^2}=\frac{47}{7}$, find the value of the ratio $\frac{b^3-2a^3}{b^3+2a^3}$.

If $\frac{3a+7b}{3a-7b}=\frac{4}{3}$, then find the value of the ratio $\frac{3a^2-7b^2}{3a^2+7b^2}$ in fraction.

Solve the following equation.

$\frac{x^2+12x-20}{3x-5}=\frac{x^2+8x+12}{2x+3}$

$x=$_____,_____

Solve the following equation and find the value of $x$.

$\frac{10x^2+15x+63}{5x^2-25x+12}=\frac{2x+3}{x-5}$

Solve the following equations.

$\frac{{\left(2x+1\right)}^2+{\left(2x-1\right)}^2}{{\left(2x+1\right)}^2-{\left(2x-1\right)}^2}=\frac{17}{8}$

Solve the following equation find value of $x$.

$\frac{\sqrt{4x+1}+\sqrt{x+3}}{\sqrt{4x+1}-\sqrt{x+3}}=\frac{4}{1}$

Solve the following equations.

$\frac{{\left(4x+1\right)}^2+{\left(2x+3\right)}^2}{4x^2+12x+9}=\frac{61}{26}$