Solve 5/277+7/92/frac{4{9}z^2+1/81z^2-z^2}

$$\frac { \frac { 5 } { 27 } 7 + \frac { 7 } { 92 } } { \frac { 4 } { 9 } z ^ { 2 } + \frac { 1 } { 81 } z ^ { 2 } - z ^ { 2 } }$$

Evaluate

$$-\frac{10227}{4048z^{2}}$$

Solution Steps

Multiply \frac{5}{27} and 7 to get \frac{35}{27}.

$$\frac{\frac{35}{27}+\frac{7}{92}}{\frac{4}{9}z^{2}+\frac{1}{81}z^{2}-z^{2}}$$

Add \frac{35}{27} and \frac{7}{92} to get \frac{3409}{2484}.

$$\frac{\frac{3409}{2484}}{\frac{4}{9}z^{2}+\frac{1}{81}z^{2}-z^{2}}$$

Combine \frac{4}{9}z^{2} and \frac{1}{81}z^{2} to get \frac{37}{81}z^{2}.

$$\frac{\frac{3409}{2484}}{\frac{37}{81}z^{2}-z^{2}}$$

Combine \frac{37}{81}z^{2} and -z^{2} to get -\frac{44}{81}z^{2}.

$$\frac{\frac{3409}{2484}}{-\frac{44}{81}z^{2}}$$

Express \frac{\frac{3409}{2484}}{-\frac{44}{81}z^{2}} as a single fraction.

$$\frac{3409}{2484\left(-\frac{44}{81}\right)z^{2}}$$

Multiply 2484 and -\frac{44}{81} to get -\frac{4048}{3}.

$$\frac{3409}{-\frac{4048}{3}z^{2}}$$

Expand

$$-\frac{10227}{4048z^{2}}$$

Solution Steps

Multiply \frac{5}{27} and 7 to get \frac{35}{27}.

$$\frac{\frac{35}{27}+\frac{7}{92}}{\frac{4}{9}z^{2}+\frac{1}{81}z^{2}-z^{2}}$$

Add \frac{35}{27} and \frac{7}{92} to get \frac{3409}{2484}.

$$\frac{\frac{3409}{2484}}{\frac{4}{9}z^{2}+\frac{1}{81}z^{2}-z^{2}}$$

Combine \frac{4}{9}z^{2} and \frac{1}{81}z^{2} to get \frac{37}{81}z^{2}.

$$\frac{\frac{3409}{2484}}{\frac{37}{81}z^{2}-z^{2}}$$

Combine \frac{37}{81}z^{2} and -z^{2} to get -\frac{44}{81}z^{2}.

$$\frac{\frac{3409}{2484}}{-\frac{44}{81}z^{2}}$$

Express \frac{\frac{3409}{2484}}{-\frac{44}{81}z^{2}} as a single fraction.

$$\frac{3409}{2484\left(-\frac{44}{81}\right)z^{2}}$$

Multiply 2484 and -\frac{44}{81} to get -\frac{4048}{3}.

$$\frac{3409}{-\frac{4048}{3}z^{2}}$$