Solve 3y^5+5y^2-12y+10divy^2+2

$$3 { y }^{ 5 } +5 { y }^{ 2 } -12y+10 \div { y }^{ 2 } +2$$

Evaluate

$$3y^{5}+5y^{2}-12y+2+\frac{10}{y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3y^{5}+5y^{2}-12y+2 times \frac{y^{2}}{y^{2}}.

$$\frac{\left(3y^{5}+5y^{2}-12y+2\right)y^{2}}{y^{2}}+\frac{10}{y^{2}}$$

Since \frac{\left(3y^{5}+5y^{2}-12y+2\right)y^{2}}{y^{2}} and \frac{10}{y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(3y^{5}+5y^{2}-12y+2\right)y^{2}+10}{y^{2}}$$

Do the multiplications in \left(3y^{5}+5y^{2}-12y+2\right)y^{2}+10.

$$\frac{3y^{7}+5y^{4}-12y^{3}+2y^{2}+10}{y^{2}}$$

Factor

$$\frac{3y^{7}+5y^{4}-12y^{3}+2y^{2}+10}{y^{2}}$$