Solve 3*(3y)^2+4*3y-y/4*(3y^2)+5(3y^2)-2y^2*2*3y+y/7*3y+y

$$\frac { 3 \cdot ( 3 y ) ^ { 2 } + 4 \cdot 3 y - y } { 4 \cdot ( 3 y ^ { 2 } ) + 5 ( 3 y ^ { 2 } ) - 2 y ^ { 2 } } \cdot \frac { 2 \cdot 3 y + y } { 7 \cdot 3 y + y }$$

Evaluate

$$\frac{189}{550}+\frac{7}{50y}$$

Short Solution Steps

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{3\times 9y^{2}+4\times 3y-y}{4\times 3y^{2}+5\times 3y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Multiply 3 and 9 to get 27.

$$\frac{27y^{2}+4\times 3y-y}{4\times 3y^{2}+5\times 3y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Multiply 4 and 3 to get 12.

$$\frac{27y^{2}+12y-y}{4\times 3y^{2}+5\times 3y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Combine 12y and -y to get 11y.

$$\frac{27y^{2}+11y}{4\times 3y^{2}+5\times 3y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Do the multiplications.

$$\frac{27y^{2}+11y}{12y^{2}+15y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Combine 12y^{2} and 15y^{2} to get 27y^{2}.

$$\frac{27y^{2}+11y}{27y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Combine 27y^{2} and -2y^{2} to get 25y^{2}.

$$\frac{27y^{2}+11y}{25y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Factor the expressions that are not already factored in \frac{27y^{2}+11y}{25y^{2}}.

$$\frac{y\left(27y+11\right)}{25y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Cancel out y in both numerator and denominator.

$$\frac{27y+11}{25y}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Multiply 2 and 3 to get 6.

$$\frac{27y+11}{25y}\times \frac{6y+y}{7\times 3y+y}$$

Combine 6y and y to get 7y.

$$\frac{27y+11}{25y}\times \frac{7y}{7\times 3y+y}$$

Multiply 7 and 3 to get 21.

$$\frac{27y+11}{25y}\times \frac{7y}{21y+y}$$

Combine 21y and y to get 22y.

$$\frac{27y+11}{25y}\times \frac{7y}{22y}$$

Cancel out y in both numerator and denominator.

$$\frac{27y+11}{25y}\times \frac{7}{22}$$

Multiply \frac{27y+11}{25y} times \frac{7}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(27y+11\right)\times 7}{25y\times 22}$$

Multiply 25 and 22 to get 550.

$$\frac{\left(27y+11\right)\times 7}{550y}$$

Use the distributive property to multiply 27y+11 by 7.

$$\frac{189y+77}{550y}$$

Expand

$$\frac{189}{550}+\frac{7}{50y}$$

Short Solution Steps

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{3\times 9y^{2}+4\times 3y-y}{4\times 3y^{2}+5\times 3y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Multiply 3 and 9 to get 27.

$$\frac{27y^{2}+4\times 3y-y}{4\times 3y^{2}+5\times 3y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Multiply 4 and 3 to get 12.

$$\frac{27y^{2}+12y-y}{4\times 3y^{2}+5\times 3y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Combine 12y and -y to get 11y.

$$\frac{27y^{2}+11y}{4\times 3y^{2}+5\times 3y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Do the multiplications.

$$\frac{27y^{2}+11y}{12y^{2}+15y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Combine 12y^{2} and 15y^{2} to get 27y^{2}.

$$\frac{27y^{2}+11y}{27y^{2}-2y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Combine 27y^{2} and -2y^{2} to get 25y^{2}.

$$\frac{27y^{2}+11y}{25y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Factor the expressions that are not already factored in \frac{27y^{2}+11y}{25y^{2}}.

$$\frac{y\left(27y+11\right)}{25y^{2}}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Cancel out y in both numerator and denominator.

$$\frac{27y+11}{25y}\times \frac{2\times 3y+y}{7\times 3y+y}$$

Multiply 2 and 3 to get 6.

$$\frac{27y+11}{25y}\times \frac{6y+y}{7\times 3y+y}$$

Combine 6y and y to get 7y.

$$\frac{27y+11}{25y}\times \frac{7y}{7\times 3y+y}$$

Multiply 7 and 3 to get 21.

$$\frac{27y+11}{25y}\times \frac{7y}{21y+y}$$

Combine 21y and y to get 22y.

$$\frac{27y+11}{25y}\times \frac{7y}{22y}$$

Cancel out y in both numerator and denominator.

$$\frac{27y+11}{25y}\times \frac{7}{22}$$

Multiply \frac{27y+11}{25y} times \frac{7}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(27y+11\right)\times 7}{25y\times 22}$$

Multiply 25 and 22 to get 550.

$$\frac{\left(27y+11\right)\times 7}{550y}$$

Use the distributive property to multiply 27y+11 by 7.

$$\frac{189y+77}{550y}$$