Solve (f(x) = -\frac{1}{x-3} - 1)

Evaluate

f x = - \frac{1}{x - 3} - 1

Multiply both sides of the equation by LCD

f x (x - 3) = (- \frac{1}{x - 3} - 1) (x - 3)

Simplify the equation

More Steps

f x^{2} - 3 f x = (- \frac{1}{x - 3} - 1) (x - 3)

Simplify the equation

More Steps

f x^{2} - 3 f x = 2 - x

Move the expression to the left side

f x^{2} - 3 f x - (2 - x) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

f x^{2} - 3 f x - 2 + x = 0

Collect like terms by calculating the sum or difference of their coefficients

f x^{2} + (- 3 f + 1) x - 2 = 0

Substitute a= f,b= - 3 f + 1 and c= - 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 f - 1 \pm ( - 3 f + 1 ) ^{2} - 4 f ( - 2 )}{2 f}

Simplify the expression

More Steps

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

Solution

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

Solve the equation