Solve (9x^4-31x^312x^2)/(x-3)

Question

Simplify the expression

\frac{9 x ^{4} - 372 x ^{5}}{x - 3}

Evaluate

\frac{9 x ^{4} - 31 x ^{3} \times 12 x ^{2}}{x - 3}

Solution

More Steps

Evaluate

31 x^{3} \times 12 x^{2}

Multiply the terms

372 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

372 x^{3 + 2}

Add the numbers

372 x^{5}

\frac{9 x ^{4} - 372 x ^{5}}{x - 3}

Show Solution

Find the excluded values

x = 3

Evaluate

\frac{9 x ^{4} - 31 x ^{3} \times 12 x ^{2}}{x - 3}

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

x - 3 = 0

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

x = 0 + 3

Solution

x = 3

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3}{124}

Alternative Form

x_{1} = 0, x_{2} \approx 0.024194

Evaluate

\frac{9 x ^{4} - 31 x ^{3} \times 12 x ^{2}}{x - 3}

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

\frac{9 x ^{4} - 31 x ^{3} \times 12 x ^{2}}{x - 3} = 0

Find the domain

More Steps

Evaluate

x - 3 \neq = 0

Move the constant to the right side

x \neq = 0 + 3

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

x \neq = 3

\frac{9 x ^{4} - 31 x ^{3} \times 12 x ^{2}}{x - 3} = 0, x \neq = 3

Calculate

\frac{9 x ^{4} - 31 x ^{3} \times 12 x ^{2}}{x - 3} = 0

Multiply

More Steps

Multiply the terms

31 x^{3} \times 12 x^{2}

Multiply the terms

372 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

372 x^{3 + 2}

Add the numbers

372 x^{5}

\frac{9 x ^{4} - 372 x ^{5}}{x - 3} = 0

Cross multiply

9 x^{4} - 372 x^{5} = (x - 3) \times 0

Simplify the equation

9 x^{4} - 372 x^{5} = 0

Factor the expression

3 x^{4} (3 - 124 x) = 0

Divide both sides

x^{4} (3 - 124 x) = 0

Separate the equation into 2 possible cases

x^{4} = 0 3 - 124 x = 0

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

x = 0 3 - 124 x = 0

Solve the equation

More Steps

Evaluate

3 - 124 x = 0

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

- 124 x = 0 - 3

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

- 124 x = - 3

Change the signs on both sides of the equation

124 x = 3

Divide both sides

\frac{124 x}{124} = \frac{3}{124}

Divide the numbers

x = \frac{3}{124}

x = 0 x = \frac{3}{124}

Check if the solution is in the defined range

x = 0 x = \frac{3}{124}, x \neq = 3

Find the intersection of the solution and the defined range

x = 0 x = \frac{3}{124}

Solution

x_{1} = 0, x_{2} = \frac{3}{124}

Alternative Form

x_{1} = 0, x_{2} \approx 0.024194

Show Solution