Solve (-4)*frac{12y_{0}-(27+4y_0^2)*y_{0}}{27-4(27+4y_{0})}+y

$$( - 4 ) \times \frac { 12 y _ { 0 } - ( 27 + 4 y _ { 0 } ^ { 2 } ) \times y _ { 0 } } { 27 - 4 ( 27 + 4 y _ { 0 } ) } + y$$

Evaluate

$$-\frac{60y_{0}+16y_{0}^{3}-81y-16yy_{0}}{16y_{0}+81}$$

Short Solution Steps

Use the distributive property to multiply 27+4y_{0}^{2} by y_{0}.

$$-4\times \frac{12y_{0}-\left(27y_{0}+4y_{0}^{3}\right)}{27-4\left(27+4y_{0}\right)}+y$$

To find the opposite of 27y_{0}+4y_{0}^{3}, find the opposite of each term.

$$-4\times \frac{12y_{0}-27y_{0}-4y_{0}^{3}}{27-4\left(27+4y_{0}\right)}+y$$

Combine 12y_{0} and -27y_{0} to get -15y_{0}.

$$-4\times \frac{-15y_{0}-4y_{0}^{3}}{27-4\left(27+4y_{0}\right)}+y$$

Use the distributive property to multiply -4 by 27+4y_{0}.

$$-4\times \frac{-15y_{0}-4y_{0}^{3}}{27-108-16y_{0}}+y$$

Subtract 108 from 27 to get -81.

$$-4\times \frac{-15y_{0}-4y_{0}^{3}}{-81-16y_{0}}+y$$

Express -4\times \frac{-15y_{0}-4y_{0}^{3}}{-81-16y_{0}} as a single fraction.

$$\frac{-4\left(-15y_{0}-4y_{0}^{3}\right)}{-81-16y_{0}}+y$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{-81-16y_{0}}{-81-16y_{0}}.

$$\frac{-4\left(-15y_{0}-4y_{0}^{3}\right)}{-81-16y_{0}}+\frac{y\left(-81-16y_{0}\right)}{-81-16y_{0}}$$

Since \frac{-4\left(-15y_{0}-4y_{0}^{3}\right)}{-81-16y_{0}} and \frac{y\left(-81-16y_{0}\right)}{-81-16y_{0}} have the same denominator, add them by adding their numerators.

$$\frac{-4\left(-15y_{0}-4y_{0}^{3}\right)+y\left(-81-16y_{0}\right)}{-81-16y_{0}}$$

Do the multiplications in -4\left(-15y_{0}-4y_{0}^{3}\right)+y\left(-81-16y_{0}\right).

$$\frac{60y_{0}+16y_{0}^{3}-81y-16yy_{0}}{-81-16y_{0}}$$

Expand

$$-\frac{60y_{0}+16y_{0}^{3}-81y-16yy_{0}}{16y_{0}+81}$$

Short Solution Steps

Use the distributive property to multiply 27+4y_{0}^{2} by y_{0}.

$$-4\times \frac{12y_{0}-\left(27y_{0}+4y_{0}^{3}\right)}{27-4\left(27+4y_{0}\right)}+y$$

To find the opposite of 27y_{0}+4y_{0}^{3}, find the opposite of each term.

$$-4\times \frac{12y_{0}-27y_{0}-4y_{0}^{3}}{27-4\left(27+4y_{0}\right)}+y$$

Combine 12y_{0} and -27y_{0} to get -15y_{0}.

$$-4\times \frac{-15y_{0}-4y_{0}^{3}}{27-4\left(27+4y_{0}\right)}+y$$

Use the distributive property to multiply -4 by 27+4y_{0}.

$$-4\times \frac{-15y_{0}-4y_{0}^{3}}{27-108-16y_{0}}+y$$

Subtract 108 from 27 to get -81.

$$-4\times \frac{-15y_{0}-4y_{0}^{3}}{-81-16y_{0}}+y$$

Express -4\times \frac{-15y_{0}-4y_{0}^{3}}{-81-16y_{0}} as a single fraction.

$$\frac{-4\left(-15y_{0}-4y_{0}^{3}\right)}{-81-16y_{0}}+y$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{-81-16y_{0}}{-81-16y_{0}}.

$$\frac{-4\left(-15y_{0}-4y_{0}^{3}\right)}{-81-16y_{0}}+\frac{y\left(-81-16y_{0}\right)}{-81-16y_{0}}$$

Since \frac{-4\left(-15y_{0}-4y_{0}^{3}\right)}{-81-16y_{0}} and \frac{y\left(-81-16y_{0}\right)}{-81-16y_{0}} have the same denominator, add them by adding their numerators.

$$\frac{-4\left(-15y_{0}-4y_{0}^{3}\right)+y\left(-81-16y_{0}\right)}{-81-16y_{0}}$$

Do the multiplications in -4\left(-15y_{0}-4y_{0}^{3}\right)+y\left(-81-16y_{0}\right).

$$\frac{60y_{0}+16y_{0}^{3}-81y-16yy_{0}}{-81-16y_{0}}$$