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asambeis [7]
3 years ago
11

SIMPLIFY THE EXPRESSION... PLEASE HELP :(

Mathematics
2 answers:
erastova [34]3 years ago
8 0

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}

EastWind [94]3 years ago
8 0

<u>Answer:</u>

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

<u>Step-by-step explanation:</u>

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} )

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