Solve ( 5*3 - 13*2 - x + 2 ) / ( x^2 - 3 x + 1 )

Question

Simplify the expression

- \frac{9 + x}{x ^{2} - 3 x + 1}

Show Solution

x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

Show Solution

x = - 9

Evaluate

\frac{5 \times 3 - 13 \times 2 - x + 2}{x ^{2} - 3 x + 1}

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

\frac{5 \times 3 - 13 \times 2 - x + 2}{x ^{2} - 3 x + 1} = 0

Find the domain

More Steps

\frac{5 \times 3 - 13 \times 2 - x + 2}{x ^{2} - 3 x + 1} = 0, x \in (- \infty, \frac{- 5 + 3}{2}) \cup (\frac{- 5 + 3}{2}, \frac{5 + 3}{2}) \cup (\frac{5 + 3}{2}, + \infty)

Calculate

\frac{5 \times 3 - 13 \times 2 - x + 2}{x ^{2} - 3 x + 1} = 0

Multiply the numbers

\frac{15 - 13 \times 2 - x + 2}{x ^{2} - 3 x + 1} = 0

Multiply the numbers

\frac{15 - 26 - x + 2}{x ^{2} - 3 x + 1} = 0

Subtract the numbers

\frac{- 11 - x + 2}{x ^{2} - 3 x + 1} = 0

Add the numbers

\frac{- 9 - x}{x ^{2} - 3 x + 1} = 0

Cross multiply

- 9 - x = (x^{2} - 3 x + 1) \times 0

Simplify the equation

- 9 - x = 0

Move the constant to the right side

- x = 0 + 9

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

- x = 9

Change the signs on both sides of the equation

x = - 9

Check if the solution is in the defined range

x = - 9, x \in (- \infty, \frac{- 5 + 3}{2}) \cup (\frac{- 5 + 3}{2}, \frac{5 + 3}{2}) \cup (\frac{5 + 3}{2}, + \infty)

Solution

x = - 9

Show Solution