Question

2x²+5xy-3y²
_________
2x²+7xy+3y²



Simplify

Answer 1

2x²+5xy-3y²

_________

2x²+7xy+3y²

Simplify

Answer 2

Answer:

( 2 x - y ) / (2 x + y )

Step-by-step explanation:

Given--->

2x² + 5 x y - 3 y²

---------------------------

2 x² + 7 x y + 3 y²

To find ---> Simplify the given expression

Solution--->

First we factrioze the numerator by splitting the middle term

2 x² + 5 x y - 3 y²

First we multiply the coefficient of x² and y² which are 2 and 3 respectively and we get 6

Now we break 6 in to two factors such that whose difference is 5 so required factors are 6 and 1

Now

2x² + 5xy - 3 y²

= 2 x² + ( 6 - 1 ) xy - 3 y²

= 2 x² + 6 xy - xy - 3 y²

= 2 x ( x + 3 y ) - y ( x + 3 y )

= ( x + 3 y ) ( 2 x - y )

Now we factrioze the denominator by splitting the middle term

2x² + 7 x y + 3 y²

First we multiply the coefficient of x² and y² which gives us 6

Now we break 6 in to two factors whose sum is 7 which are 6 and 1

Now

2x² + 7 x y + 3 y²

= 2 x² + ( 6 + 1 ) xy + 3 y²

= 2 x² + 6 xy + xy + 3 y²

= 2 x ( x + 3 y ) + y ( x + 3 y )

= ( x + 3 y ) ( 2 x + y )

Now we simplify given expression

2 x² + 5 x y - 3 y²

---------------------------

2 x² + 7 x y + 3 y²

Putting factors of numerator and denominator

( x + 3 y ) ( 2 x - y )

= ----------------------------------

( x + 3 y ) ( 2 x + y )

( x + 3 y ) cancel out from numerator and denominator

( 2 x - y )

= ------------------

( 2 x + y )