Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

Simplify $\frac{x^2+2 x+y^2}{x^3-5 x^2}$ if $x+\frac{y^2}{x}=5$.

Options:

$\frac{5}{y^2}$

$\frac{7}{y^2}$

$-\frac{5}{y^2}$

$-\frac{7}{y^2}$

Correct Answer:

$-\frac{7}{y^2}$

Explanation:

Simplify $\frac{x^2+2 x+y^2}{x^3-5 x^2}$ 

If $x+\frac{y^2}{x}=5$

then x2 + y2 = 5x put in $\frac{x^2+2 x+y^2}{x^3-5 x^2}$ 

= $\frac{5x +2 x}{x(x^2-5 x)}$ 

= \(\frac{5x +2 x}{x(x^2-x^2 + y^2)}\)

= \(\frac{7x}{-xy^2}\) = $-\frac{7}{y^2}$