Question

SIMPLIFY THE EXPRESSION... PLEASE HELP :(

Answer 1

remember $\frac{\frac{a}{b}}{\frac{c}{d}}=(\frac{a}{b})(\frac{d}{c})=\frac{ad}{bc}$

try to combine fractions in numerator and denomenator

numerator: $\frac{1}{x}+\frac{2}{y}$

make common denom

multiply left one by $\frac{y}{y}$ and right one by $\frac{x^2}{x^2}$

$\frac{y}{yx^2}+\frac{2x^2}{yx^2}=\frac{2x^2+y}{yx^2}$

denomenator

$\frac{5}{x}-\frac{6}{y^2}$

make common denom

multiply left one by $\frac{y^2}{y^2}$ and right one by $\frac{x}{x}$

$\frac{5y^2}{xy^2}-\frac{6x}{xy^2}=\frac{5y^2-6x}{xy^2}$

combining we get

$\frac{\frac{1}{x^2}+\frac{2}{y}}{\frac{5}{x}-\frac{6}{y^2}}=$

$\frac{\frac{2x^2+y}{yx^2}}{\frac{-6x+5y^2}{xy^2}}=$

$(\frac{2x^2+y}{yx^2})(\frac{xy^2}{-6x+5y^2})=$

$\frac{2x^3y^2+xy^3}{-6x^3y+5x^2y^3}=$

$(\frac{2x^2y+y^2}{-6x^2+5xy})(\frac{xy}{xy})=$

$(\frac{2x^2y+y^2}{-6x^2+5xy})(1)=$

$\frac{2x^2y+y^2}{-6x^2+5xy}$

Answer 2

Answer:

The simplified version of the given expression is $(\frac{2x^2y+y^2}{5xy-6x^2} )$

Step-by-step explanation:

We are given an expression which is a complex fraction:

$\frac{\frac{1}{x^2} +\frac{2}{y} }{\frac{5}{x} +\frac{6}{y^2} }$

We can take LCM of these fractions to get:

$\frac{\frac{y+2x^2}{x^2y} }{\frac{5y^2-6x}{xy^2} }$

Taking the reciprocal of the lower fraction to change it to multiplication:

$\frac{y+2x^2}{x^2y}$ × $\frac{xy^2}{5y^2-6x}$

$\frac{2x^2y+xy^3}{5x^2y^3-6x^3y}$

Taking xy as common from both the numerator and the denominator to get:

$\frac{xy}{xy} (\frac{2x^2y+y^2}{5xy-6x^2} )$

$(\frac{2x^2y+y^2}{5xy-6x^2} )$