What is (x^2+xy^2)/(2y^2+1)+3 ?

The solution to (x^2+xy^2)/(2y^2+1)+3 is (6y^2+3+x^2+xy^2)/(2y^2+1)

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simplify (x^2+xy^2)/(2y^2+1)+3

simplify

\frac{x ^{2} + x y ^{2}}{2 y ^{2} + 1} + 3

\frac{6 y ^{2} + 3 + x ^{2} + x y ^{2}}{2 y ^{2} + 1}

Solution steps

\frac{x ^{2} + x y ^{2}}{2 y ^{2} + 1} + 3

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

= \frac{3 ( 2 y ^{2} + 1 ) + x ^{2} + x y ^{2}}{2 y ^{2} + 1}

Simplify

3 (2 y^{2} + 1) + x^{2} + x y^{2} : 6 y^{2} + 3 + x^{2} + x y^{2}

= \frac{6 y ^{2} + 3 + x ^{2} + x y ^{2}}{2 y ^{2} + 1}

\frac{2 ( \frac{4 x + 5}{2} ) - 5}{4}

5 x - 80 x^{3}

144 x^{2} y^{5}

(1 - 3 x)^{3}

(z - 2)^{3}

What is (x^2+xy^2)/(2y^2+1)+3 ?
The solution to (x^2+xy^2)/(2y^2+1)+3 is (6y^2+3+x^2+xy^2)/(2y^2+1)