Solve (x^2-9x 18)/(x-6)

Question

Simplify the expression

\frac{x ^{2} - 162 x}{x - 6}

Evaluate

\frac{x ^{2} - 9 x \times 18}{x - 6}

Solution

\frac{x ^{2} - 162 x}{x - 6}

Show Solution

x = 6

Evaluate

\frac{x ^{2} - 9 x \times 18}{x - 6}

To find the excluded values,set the denominators equal to 0

x - 6 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 6

Solution

x = 6

Show Solution

x_{1} = 0, x_{2} = 162

Evaluate

\frac{x ^{2} - 9 x \times 18}{x - 6}

To find the roots of the expression,set the expression equal to 0

\frac{x ^{2} - 9 x \times 18}{x - 6} = 0

Find the domain

More Steps

Evaluate

x - 6 \neq = 0

Move the constant to the right side

x \neq = 0 + 6

Removing 0 doesn't change the value,so remove it from the expression

x \neq = 6

\frac{x ^{2} - 9 x \times 18}{x - 6} = 0, x \neq = 6

Calculate

\frac{x ^{2} - 9 x \times 18}{x - 6} = 0

Multiply the terms

\frac{x ^{2} - 162 x}{x - 6} = 0

Cross multiply

x^{2} - 162 x = (x - 6) \times 0

Simplify the equation

x^{2} - 162 x = 0

Factor the expression

More Steps

Evaluate

x^{2} - 162 x

Rewrite the expression

x \times x - x \times 162

Factor out x from the expression

x (x - 162)

x (x - 162) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 x - 162 = 0

Solve the equation for x

More Steps

Evaluate

x - 162 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 162

Removing 0 doesn't change the value,so remove it from the expression

x = 162

x = 0 x = 162

Check if the solution is in the defined range

x = 0 x = 162, x \neq = 6

Find the intersection of the solution and the defined range

x = 0 x = 162

Solution

x_{1} = 0, x_{2} = 162

Show Solution