Solve ((x-4)(x 1)(x^2)(x^4))/((x-1)(x^2)(x-2))

Question

Simplify the expression

\frac{x ^{6} - 4 x ^{5}}{x ^{2} - 3 x + 2}

Show Solution

x = 0, x = 1, x = 2

Show Solution

x = 4

Evaluate

((x - 4) (x \times 1) (x^{2}) (x^{4})) \div ((x - 1) (x^{2}) (x - 2))

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

((x - 4) (x \times 1) (x^{2}) (x^{4})) \div ((x - 1) (x^{2}) (x - 2)) = 0

Find the domain

More Steps

((x - 4) (x \times 1) (x^{2}) (x^{4})) \div ((x - 1) (x^{2}) (x - 2)) = 0, x \in (- \infty, 0) \cup (0, 1) \cup (1, 2) \cup (2, + \infty)

Calculate

((x - 4) (x \times 1) (x^{2}) (x^{4})) \div ((x - 1) (x^{2}) (x - 2)) = 0

Any expression multiplied by 1 remains the same

((x - 4) x (x^{2}) (x^{4})) \div ((x - 1) (x^{2}) (x - 2)) = 0

Calculate

((x - 4) x \times x^{2} (x^{4})) \div ((x - 1) (x^{2}) (x - 2)) = 0

Calculate

((x - 4) x \times x^{2} \times x^{4}) \div ((x - 1) (x^{2}) (x - 2)) = 0

Multiply the terms

More Steps

x^{7} (x - 4) \div ((x - 1) (x^{2}) (x - 2)) = 0

Calculate

x^{7} (x - 4) \div ((x - 1) x^{2} (x - 2)) = 0

Multiply the first two terms

x^{7} (x - 4) \div x^{2} (x - 1) (x - 2) = 0

Divide the terms

More Steps

\frac{x ^{5} ( x - 4 )}{( x - 1 ) ( x - 2 )} = 0

Cross multiply

x^{5} (x - 4) = (x - 1) (x - 2) \times 0

Simplify the equation

x^{5} (x - 4) = 0

Separate the equation into 2 possible cases

x^{5} = 0 x - 4 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x - 4 = 0

Solve the equation

More Steps

x = 0 x = 4

Check if the solution is in the defined range

x = 0 x = 4, x \in (- \infty, 0) \cup (0, 1) \cup (1, 2) \cup (2, + \infty)

Solution

x = 4

Show Solution