Question 43

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

Solution

Given that If $$\frac{x}{y}=\frac{7}{4}$$

Therefore, $$(\frac{x}{y})^2=\frac{49}{16}$$ ... (1)

$$\dfrac{x^{2}-y^{2}}{x^{2}+y^{2}}$$ this can be written as,

$$\Rightarrow$$ $$\dfrac{(\frac{x}{y})^2-1}{(\frac{x}{y})^2+1}$$

$$\Rightarrow$$ $$\dfrac{\frac{49}{16}-1}{\frac{49}{16}+1}$$

$$\Rightarrow$$ $$\dfrac{49-16}{49+16}$$

$$\Rightarrow$$ $$\dfrac{33}{65}$$

Hence, option C is the correct answer.

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