Solve (x-1)(x-2)/(5-1)(5-2(10)

$$\frac { ( x - 1 ) ( x - 2 ) } { ( 5 - 1 ) ( 5 - 2 } ( 10 )$$

Evaluate

$$\frac{5\left(x-2\right)\left(x-1\right)}{6}$$

Solution Steps

Subtract 1 from 5 to get 4.

$$\frac{\left(x-1\right)\left(x-2\right)}{4\left(5-2\right)}\times 10$$

Subtract 2 from 5 to get 3.

$$\frac{\left(x-1\right)\left(x-2\right)}{4\times 3}\times 10$$

Multiply 4 and 3 to get 12.

$$\frac{\left(x-1\right)\left(x-2\right)}{12}\times 10$$

Express \frac{\left(x-1\right)\left(x-2\right)}{12}\times 10 as a single fraction.

$$\frac{\left(x-1\right)\left(x-2\right)\times 10}{12}$$

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

$$\frac{\left(x^{2}-2x-x+2\right)\times 10}{12}$$

Combine -2x and -x to get -3x.

$$\frac{\left(x^{2}-3x+2\right)\times 10}{12}$$

Use the distributive property to multiply x^{2}-3x+2 by 10.

$$\frac{10x^{2}-30x+20}{12}$$

Expand

$$\frac{5x^{2}}{6}-\frac{5x}{2}+\frac{5}{3}$$

Solution Steps

Subtract 1 from 5 to get 4.

$$\frac{\left(x-1\right)\left(x-2\right)}{4\left(5-2\right)}\times 10$$

Subtract 2 from 5 to get 3.

$$\frac{\left(x-1\right)\left(x-2\right)}{4\times 3}\times 10$$

Multiply 4 and 3 to get 12.

$$\frac{\left(x-1\right)\left(x-2\right)}{12}\times 10$$

Express \frac{\left(x-1\right)\left(x-2\right)}{12}\times 10 as a single fraction.

$$\frac{\left(x-1\right)\left(x-2\right)\times 10}{12}$$

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

$$\frac{\left(x^{2}-2x-x+2\right)\times 10}{12}$$

Combine -2x and -x to get -3x.

$$\frac{\left(x^{2}-3x+2\right)\times 10}{12}$$

Use the distributive property to multiply x^{2}-3x+2 by 10.

$$\frac{10x^{2}-30x+20}{12}$$