Question

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

Answer 1

`\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)}}`