Question

If $\frac{4x+3y}{4x-3y}=\frac{7}{4}$, use the properties to find the value of $\frac{2x^2-11y^2}{2x^2+11y^2}$

Answer 1

$\frac{4x+3y}{4x-3y}=\frac{7}{4}$

So,

$\frac{4x+3y+(4x-3y)}{4x+3y-(4x-3y)}=\frac{7+4}{7-4}$

$\frac{8x}{6y}=\frac{11}{3}$

$\frac{4x}{3y}=\frac{11}{3}$

$\frac{x}{y}=\frac{11}{3}\times \frac{3}{4}$

$\frac{x}{y}=\frac{11}{4}$

Square both sides,

${\left(\frac{x}{y}\right)}^2={\left(\frac{11}{4}\right)}^2$

$\frac{x^2}{y^2}=\frac{121}{16}$

$\frac{2x^2}{11y^2}=\frac{121}{16}\times \frac{2}{11}=\frac{11}{8}$

$\Rightarrow \frac{2x^2-11y^2}{2x^2+11y^2}=\frac{11-8}{11+8}=\frac{3}{19}$