Solve 5/2x-18*2/5x-45

$$\frac { 5 } { 2 x - 18 } \cdot \frac { 2 } { 5 x - 45 }$$

Evaluate

$$\frac{1}{\left(x-9\right)^{2}}$$

Solution Steps

Multiply \frac{5}{2x-18} times \frac{2}{5x-45} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 2}{\left(2x-18\right)\left(5x-45\right)}$$

Multiply 5 and 2 to get 10.

$$\frac{10}{\left(2x-18\right)\left(5x-45\right)}$$

Apply the distributive property by multiplying each term of 2x-18 by each term of 5x-45.

$$\frac{10}{10x^{2}-90x-90x+810}$$

Combine -90x and -90x to get -180x.

$$\frac{10}{10x^{2}-180x+810}$$

Differentiate w.r.t. x

$$-\frac{2}{\left(x-9\right)^{3}}$$