Solve frac{5(3z)^{2}+2(2z)^{2}-8^2}{2(3z)^2-3(2z)^2-10z^2}

$$\frac { 5 ( 3 z ) ^ { 2 } + 2 ( 2 z ) ^ { 2 } - 8 ^ { 2 } } { 2 ( 3 z ) ^ { 2 } - 3 ( 2 z ) ^ { 2 } - 10 z ^ { 2 } }$$

Evaluate

$$-\frac{53}{4}+\frac{16}{z^{2}}$$

Solution Steps

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

$$\frac{5\times 3^{2}z^{2}+2\times \left(2z\right)^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{5\times 9z^{2}+2\times \left(2z\right)^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Multiply 5 and 9 to get 45.

$$\frac{45z^{2}+2\times \left(2z\right)^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Expand \left(2z\right)^{2}.

$$\frac{45z^{2}+2\times 2^{2}z^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{45z^{2}+2\times 4z^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Multiply 2 and 4 to get 8.

$$\frac{45z^{2}+8z^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Combine 45z^{2} and 8z^{2} to get 53z^{2}.

$$\frac{53z^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{53z^{2}-64}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

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

$$\frac{53z^{2}-64}{2\times 3^{2}z^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{53z^{2}-64}{2\times 9z^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Multiply 2 and 9 to get 18.

$$\frac{53z^{2}-64}{18z^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Expand \left(2z\right)^{2}.

$$\frac{53z^{2}-64}{18z^{2}-3\times 2^{2}z^{2}-10z^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{53z^{2}-64}{18z^{2}-3\times 4z^{2}-10z^{2}}$$

Multiply 3 and 4 to get 12.

$$\frac{53z^{2}-64}{18z^{2}-12z^{2}-10z^{2}}$$

Combine 18z^{2} and -12z^{2} to get 6z^{2}.

$$\frac{53z^{2}-64}{6z^{2}-10z^{2}}$$

Combine 6z^{2} and -10z^{2} to get -4z^{2}.

$$\frac{53z^{2}-64}{-4z^{2}}$$

Expand

$$-\frac{53}{4}+\frac{16}{z^{2}}$$

Solution Steps

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

$$\frac{5\times 3^{2}z^{2}+2\times \left(2z\right)^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{5\times 9z^{2}+2\times \left(2z\right)^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Multiply 5 and 9 to get 45.

$$\frac{45z^{2}+2\times \left(2z\right)^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Expand \left(2z\right)^{2}.

$$\frac{45z^{2}+2\times 2^{2}z^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{45z^{2}+2\times 4z^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Multiply 2 and 4 to get 8.

$$\frac{45z^{2}+8z^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Combine 45z^{2} and 8z^{2} to get 53z^{2}.

$$\frac{53z^{2}-8^{2}}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{53z^{2}-64}{2\times \left(3z\right)^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

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

$$\frac{53z^{2}-64}{2\times 3^{2}z^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{53z^{2}-64}{2\times 9z^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Multiply 2 and 9 to get 18.

$$\frac{53z^{2}-64}{18z^{2}-3\times \left(2z\right)^{2}-10z^{2}}$$

Expand \left(2z\right)^{2}.

$$\frac{53z^{2}-64}{18z^{2}-3\times 2^{2}z^{2}-10z^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{53z^{2}-64}{18z^{2}-3\times 4z^{2}-10z^{2}}$$

Multiply 3 and 4 to get 12.

$$\frac{53z^{2}-64}{18z^{2}-12z^{2}-10z^{2}}$$

Combine 18z^{2} and -12z^{2} to get 6z^{2}.

$$\frac{53z^{2}-64}{6z^{2}-10z^{2}}$$

Combine 6z^{2} and -10z^{2} to get -4z^{2}.

$$\frac{53z^{2}-64}{-4z^{2}}$$