Solve 4z/(z-5)(z+5)*z+5/z

$$\frac { 4 z } { ( z - 5 ) ( z + 5 ) } \cdot \frac { z + 5 } { z }$$

Evaluate

$$\frac{4}{z-5}$$

Short Solution Steps

Consider \left(z-5\right)\left(z+5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{4z}{z^{2}-5^{2}}\times \frac{z+5}{z}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4z}{z^{2}-25}\times \frac{z+5}{z}$$

Multiply \frac{4z}{z^{2}-25} times \frac{z+5}{z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4z\left(z+5\right)}{\left(z^{2}-25\right)z}$$

Cancel out z in both numerator and denominator.

$$\frac{4\left(z+5\right)}{z^{2}-25}$$

Factor the expressions that are not already factored.

$$\frac{4\left(z+5\right)}{\left(z-5\right)\left(z+5\right)}$$

Cancel out z+5 in both numerator and denominator.

$$\frac{4}{z-5}$$

Expand

$$\frac{4}{z-5}$$

Short Solution Steps

Consider \left(z-5\right)\left(z+5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{4z}{z^{2}-5^{2}}\times \frac{z+5}{z}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4z}{z^{2}-25}\times \frac{z+5}{z}$$

Multiply \frac{4z}{z^{2}-25} times \frac{z+5}{z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4z\left(z+5\right)}{\left(z^{2}-25\right)z}$$

Cancel out z in both numerator and denominator.

$$\frac{4\left(z+5\right)}{z^{2}-25}$$

Factor the expressions that are not already factored.

$$\frac{4\left(z+5\right)}{\left(z-5\right)\left(z+5\right)}$$

Cancel out z+5 in both numerator and denominator.

$$\frac{4}{z-5}$$