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6 votes
How do you simplify this?
x²y+xy² / y²+2/5 × xy​​

User Ella Ryan
by
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1 Answer

13 votes
13 votes


\huge \boxed{\mathbb{QUESTION} \downarrow}

  • How do you simplify this ⇨ x²y+xy² / y²+2/5 × xy


\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}


\sf\frac{ { x }^( 2 ) y+x { y }^( 2 ) }{ { y }^( 2 ) + ( 2 )/( 5 ) * xy } \\

Factor the expressions that are not already factored.

_____

How to factorise :-

NUMERATOR
\downarrow


\sf \: x ^ { 2 } y + x y ^ { 2 }

Factor out xy.


\sf \: xy\left(x+y\right)

DENOMINATOR
\downarrow


\sf{ y }^( 2 ) + ( 2 )/( 5 ) * xy \\

Factor out 1/5.


\sf \: {(1)/(5)y\left(2x+5y\right)} \\

_____

Continuing...


\sf(xy\left(x+y\right))/((1)/(5)y\left(2x+5y\right)) \\

Cancel out y in both the numerator and denominator.


\sf(x\left(x+y\right))/((1)/(5)\left(2x+5y\right)) \\

Expand the expression.


\sf(x^(2)+xy)/((2)/(5)x+y) \\

This can further simplified to as
\downarrow


= \boxed{\boxed{\bf(5x\left(x +y\right))/(2x+5y)}}

User JeanVuda
by
2.7k points