Solve frac{9y-33y^{2}-3y^4}{100-49y^2}*7y^2+17y+10/14y^2+28y

$$\frac { 9 y - 33 y ^ { 2 } - 3 y ^ { 4 } } { 100 - 49 y ^ { 2 } } \cdot \frac { 7 y ^ { 2 } + 17 y + 10 } { 14 y ^ { 2 } + 28 y }$$

Evaluate

$$-\frac{3\left(y+1\right)\left(3-11y-y^{3}\right)}{14\left(7y-10\right)\left(y+2\right)}$$

Short Solution Steps

Multiply \frac{9y-33y^{2}-3y^{4}}{100-49y^{2}} times \frac{7y^{2}+17y+10}{14y^{2}+28y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9y-33y^{2}-3y^{4}\right)\left(7y^{2}+17y+10\right)}{\left(100-49y^{2}\right)\left(14y^{2}+28y\right)}$$

Factor the expressions that are not already factored.

$$\frac{3y\left(y+1\right)\left(7y+10\right)\left(-y^{3}-11y+3\right)}{14y\left(-7y-10\right)\left(7y-10\right)\left(y+2\right)}$$

Extract the negative sign in 10+7y.

$$\frac{-3y\left(-7y-10\right)\left(y+1\right)\left(-y^{3}-11y+3\right)}{14y\left(-7y-10\right)\left(7y-10\right)\left(y+2\right)}$$

Cancel out y\left(-7y-10\right) in both numerator and denominator.

$$\frac{-3\left(y+1\right)\left(-y^{3}-11y+3\right)}{14\left(7y-10\right)\left(y+2\right)}$$

Expand the expression.

$$\frac{3y^{4}+3y^{3}+33y^{2}+24y-9}{98y^{2}+56y-280}$$

Expand

$$\frac{3\left(y^{4}+y^{3}+11y^{2}+8y-3\right)}{14\left(7y-10\right)\left(y+2\right)}$$

Short Solution Steps

Multiply \frac{9y-33y^{2}-3y^{4}}{100-49y^{2}} times \frac{7y^{2}+17y+10}{14y^{2}+28y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9y-33y^{2}-3y^{4}\right)\left(7y^{2}+17y+10\right)}{\left(100-49y^{2}\right)\left(14y^{2}+28y\right)}$$

Factor the expressions that are not already factored.

$$\frac{3y\left(y+1\right)\left(7y+10\right)\left(-y^{3}-11y+3\right)}{14y\left(-7y-10\right)\left(7y-10\right)\left(y+2\right)}$$

Extract the negative sign in 10+7y.

$$\frac{-3y\left(-7y-10\right)\left(y+1\right)\left(-y^{3}-11y+3\right)}{14y\left(-7y-10\right)\left(7y-10\right)\left(y+2\right)}$$

Cancel out y\left(-7y-10\right) in both numerator and denominator.

$$\frac{-3\left(y+1\right)\left(-y^{3}-11y+3\right)}{14\left(7y-10\right)\left(y+2\right)}$$

Expand the expression.

$$\frac{3y^{4}+3y^{3}+33y^{2}+24y-9}{98y^{2}+56y-280}$$