Solve 6y^2+2y/3y-4-9y-7/y^2

$$\frac { 6 y ^ { 2 } + 2 y } { 3 y - 4 } - \frac { 9 y - 7 } { y ^ { 2 } }$$

Evaluate

$$\frac{6y^{4}+2y^{3}-27y^{2}+57y-28}{\left(3y-4\right)y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y-4 and y^{2} is \left(3y-4\right)y^{2}. Multiply \frac{6y^{2}+2y}{3y-4} times \frac{y^{2}}{y^{2}}. Multiply \frac{9y-7}{y^{2}} times \frac{3y-4}{3y-4}.

$$\frac{\left(6y^{2}+2y\right)y^{2}}{\left(3y-4\right)y^{2}}-\frac{\left(9y-7\right)\left(3y-4\right)}{\left(3y-4\right)y^{2}}$$

Since \frac{\left(6y^{2}+2y\right)y^{2}}{\left(3y-4\right)y^{2}} and \frac{\left(9y-7\right)\left(3y-4\right)}{\left(3y-4\right)y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(6y^{2}+2y\right)y^{2}-\left(9y-7\right)\left(3y-4\right)}{\left(3y-4\right)y^{2}}$$

Do the multiplications in \left(6y^{2}+2y\right)y^{2}-\left(9y-7\right)\left(3y-4\right).

$$\frac{6y^{4}+2y^{3}-27y^{2}+36y+21y-28}{\left(3y-4\right)y^{2}}$$

Combine like terms in 6y^{4}+2y^{3}-27y^{2}+36y+21y-28.

$$\frac{6y^{4}+2y^{3}-27y^{2}+57y-28}{\left(3y-4\right)y^{2}}$$

Expand \left(3y-4\right)y^{2}.

$$\frac{6y^{4}+2y^{3}-27y^{2}+57y-28}{3y^{3}-4y^{2}}$$

Expand

$$\frac{6y^{4}+2y^{3}-27y^{2}+57y-28}{\left(3y-4\right)y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y-4 and y^{2} is \left(3y-4\right)y^{2}. Multiply \frac{6y^{2}+2y}{3y-4} times \frac{y^{2}}{y^{2}}. Multiply \frac{9y-7}{y^{2}} times \frac{3y-4}{3y-4}.

$$\frac{\left(6y^{2}+2y\right)y^{2}}{\left(3y-4\right)y^{2}}-\frac{\left(9y-7\right)\left(3y-4\right)}{\left(3y-4\right)y^{2}}$$

Since \frac{\left(6y^{2}+2y\right)y^{2}}{\left(3y-4\right)y^{2}} and \frac{\left(9y-7\right)\left(3y-4\right)}{\left(3y-4\right)y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(6y^{2}+2y\right)y^{2}-\left(9y-7\right)\left(3y-4\right)}{\left(3y-4\right)y^{2}}$$

Do the multiplications in \left(6y^{2}+2y\right)y^{2}-\left(9y-7\right)\left(3y-4\right).

$$\frac{6y^{4}+2y^{3}-27y^{2}+36y+21y-28}{\left(3y-4\right)y^{2}}$$

Combine like terms in 6y^{4}+2y^{3}-27y^{2}+36y+21y-28.

$$\frac{6y^{4}+2y^{3}-27y^{2}+57y-28}{\left(3y-4\right)y^{2}}$$

Expand \left(3y-4\right)y^{2}.

$$\frac{6y^{4}+2y^{3}-27y^{2}+57y-28}{3y^{3}-4y^{2}}$$