Question

Find the sum. Express your answer in simplest form.

Answer 1

Answer:

$\frac{10x^2+3}{y^2+4}$

Step-by-step 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 $\frac{6x^2+5}{y^2+4} +\frac{4x^2-2}{y^2+4} =\frac{(6x^2+5)+(4x^2-2)}{y^2+4}$

==> remove parenthesis and apply signs

$\frac{x^2+5+4x^2-2}{y^2+4}$

==> simplify numerator by combining like terms

$\frac{10x^2+3}{y^2+4}$

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)

Answer 2

Answer:

$\frac{10x^{2} +3}{y^{2}+4 }$

Step-by-step explanation:

$\frac{6x^{2} +5}{y^{2}+4 } +\frac{4x^{2} -2}{y^{2}+4 }$

make the common denominator

$\frac{6x^{2} +5+4x-2}{y^{2}+4 }$

combone the like terms

$\frac{10x^{2} +5-2}{y^{2}+4 }$

subtract numbers

$\frac{10x^{2} +3}{y^{2}+4 }$