Question

Find the sum. Express your answer in simplest form.

Answer 1

`(10x^(2) +3)/(y^(2)+4 )`

Explanation:

`(6x^(2) +5)/(y^(2)+4 ) +(4x^(2) -2)/(y^(2)+4 )`

make the common denominator

`(6x^(2) +5+4x-2)/(y^(2)+4 )`

combone the like terms

`(10x^(2) +5-2)/(y^(2)+4 )`

subtract numbers

`(10x^(2) +3)/(y^(2)+4 )`

Answer 2

`(10x^2+3)/(y^2+4)`

Explanation:

When adding rational numbers, if the denominator is the same you simply keep the denominator (bottom of fraction) as it is and apply the operation given to the numerator ( top of fraction )

So we have
`(6x^2+5)/(y^2+4) +(4x^2-2)/(y^2+4) =((6x^2+5)+(4x^2-2))/(y^2+4)`

==> remove parenthesis and apply signs

`(x^2+5+4x^2-2)/(y^2+4)`

==> simplify numerator by combining like terms

`(10x^2+3)/(y^2+4)`

and we are done!

Note:

like terms are terms with the same variable and exponent

An example of like terms are 6x^7 and 3x^7 as they have x as a variable and a power of 7

The like terms being combined here were (6x² and 4x²) and (5 and -2)