Solve z + 6 * z/(z + 6) * (z - 3 ^ 4)/z | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$z+6\times\frac{z}{z+6}\cdot\frac{z-3^{4}}{z}$$

Evaluate

$\frac{z^{2}+12z-486}{z+6}$

Short Solution Steps

Calculate $3$ to the power of $4$ and get $81$.

$$z+6\times \frac{z}{z+6}\times \frac{z-81}{z}$$

Express $6\times \frac{z}{z+6}$ as a single fraction.

$$z+\frac{6z}{z+6}\times \frac{z-81}{z}$$

Multiply $\frac{6z}{z+6}$ times $\frac{z-81}{z}$ by multiplying numerator times numerator and denominator times denominator.

$$z+\frac{6z\left(z-81\right)}{\left(z+6\right)z}$$

Cancel out $z$ in both numerator and denominator.

$$z+\frac{6\left(z-81\right)}{z+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $z$ times $\frac{z+6}{z+6}$.

$$\frac{z\left(z+6\right)}{z+6}+\frac{6\left(z-81\right)}{z+6}$$

Since $\frac{z\left(z+6\right)}{z+6}$ and $\frac{6\left(z-81\right)}{z+6}$ have the same denominator, add them by adding their numerators.

$$\frac{z\left(z+6\right)+6\left(z-81\right)}{z+6}$$

Do the multiplications in $z\left(z+6\right)+6\left(z-81\right)$.

$$\frac{z^{2}+6z+6z-486}{z+6}$$

Combine like terms in $z^{2}+6z+6z-486$.

$$\frac{z^{2}+12z-486}{z+6}$$

Expand

$\frac{z^{2}+12z-486}{z+6}$

Short Solution Steps

Calculate $3$ to the power of $4$ and get $81$.

$$z+6\times \frac{z}{z+6}\times \frac{z-81}{z}$$

Express $6\times \frac{z}{z+6}$ as a single fraction.

$$z+\frac{6z}{z+6}\times \frac{z-81}{z}$$

Multiply $\frac{6z}{z+6}$ times $\frac{z-81}{z}$ by multiplying numerator times numerator and denominator times denominator.

$$z+\frac{6z\left(z-81\right)}{\left(z+6\right)z}$$

Cancel out $z$ in both numerator and denominator.

$$z+\frac{6\left(z-81\right)}{z+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $z$ times $\frac{z+6}{z+6}$.

$$\frac{z\left(z+6\right)}{z+6}+\frac{6\left(z-81\right)}{z+6}$$

Since $\frac{z\left(z+6\right)}{z+6}$ and $\frac{6\left(z-81\right)}{z+6}$ have the same denominator, add them by adding their numerators.

$$\frac{z\left(z+6\right)+6\left(z-81\right)}{z+6}$$

Do the multiplications in $z\left(z+6\right)+6\left(z-81\right)$.

$$\frac{z^{2}+6z+6z-486}{z+6}$$

Combine like terms in $z^{2}+6z+6z-486$.

$$\frac{z^{2}+12z-486}{z+6}$$