Solve (12x^(2) 11x^2)/(3x^(2) 13x-10) ⋅ (15x^(2)-10x)

Question

Simplify the expression

\frac{1980 x ^{6} - 1320 x ^{5}}{39 x ^{3} - 624 x ^{5} - 10 + 160 x ^{2}}

Evaluate

(12 x^{2} \times 11 x^{2}) \div (3 x^{2} \times 13 x - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2})

Multiply

More Steps

132 x^{4} \div (3 x^{2} \times 13 x - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2})

Multiply

More Steps

132 x^{4} \div (39 x^{3} - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2})

Rewrite the expression

\frac{132 x ^{4}}{39 x ^{3} - 10} \times (15 x^{2} - 10 x) \div (1 - 16 x^{2})

Multiply the terms

\frac{132 x ^{4} ( 15 x ^{2} - 10 x )}{39 x ^{3} - 10} \div (1 - 16 x^{2})

Multiply by the reciprocal

\frac{132 x ^{4} ( 15 x ^{2} - 10 x )}{39 x ^{3} - 10} \times \frac{1}{1 - 16 x ^{2}}

Multiply the terms

\frac{132 x ^{4} ( 15 x ^{2} - 10 x )}{( 39 x ^{3} - 10 ) ( 1 - 16 x ^{2} )}

Multiply the terms

More Steps

\frac{1980 x ^{6} - 1320 x ^{5}}{( 39 x ^{3} - 10 ) ( 1 - 16 x ^{2} )}

Solution

More Steps

\frac{1980 x ^{6} - 1320 x ^{5}}{39 x ^{3} - 624 x ^{5} - 10 + 160 x ^{2}}

Show Solution

Find the excluded values

x = \frac{3 15210}{39}, x = \frac{1}{4}, x = - \frac{1}{4}

Evaluate

(12 x^{2} \times 11 x^{2}) \div (3 x^{2} \times 13 x - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2})

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

3 x^{2} \times 13 x - 10 = 0 1 - 16 x^{2} = 0

Solve the equations

More Steps

x = \frac{3 15210}{39} 1 - 16 x^{2} = 0

Solve the equations

More Steps

x = \frac{3 15210}{39} x = \frac{1}{4} x = - \frac{1}{4}

Solution

x = \frac{3 15210}{39}, x = \frac{1}{4}, x = - \frac{1}{4}

Show Solution

Find the roots

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

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{6}

Evaluate

(12 x^{2} \times 11 x^{2}) \div (3 x^{2} \times 13 x - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2})

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

(12 x^{2} \times 11 x^{2}) \div (3 x^{2} \times 13 x - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2}) = 0

Find the domain

More Steps

(12 x^{2} \times 11 x^{2}) \div (3 x^{2} \times 13 x - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2}) = 0, x \in (- \infty, - \frac{1}{4}) \cup (- \frac{1}{4}, \frac{1}{4}) \cup (\frac{1}{4}, \frac{3 15210}{39}) \cup (\frac{3 15210}{39}, + \infty)

Calculate

(12 x^{2} \times 11 x^{2}) \div (3 x^{2} \times 13 x - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2}) = 0

Multiply

More Steps

132 x^{4} \div (3 x^{2} \times 13 x - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2}) = 0

Multiply

More Steps

132 x^{4} \div (39 x^{3} - 10) (15 x^{2} - 10 x) \div (1 - 16 x^{2}) = 0

Rewrite the expression

\frac{132 x ^{4}}{39 x ^{3} - 10} \times (15 x^{2} - 10 x) \div (1 - 16 x^{2}) = 0

Multiply the terms

\frac{132 x ^{4} ( 15 x ^{2} - 10 x )}{39 x ^{3} - 10} \div (1 - 16 x^{2}) = 0

Divide the terms

More Steps

\frac{132 x ^{4} ( 15 x ^{2} - 10 x )}{( 39 x ^{3} - 10 ) ( 1 - 16 x ^{2} )} = 0

Cross multiply

132 x^{4} (15 x^{2} - 10 x) = (39 x^{3} - 10) (1 - 16 x^{2}) \times 0

Simplify the equation

132 x^{4} (15 x^{2} - 10 x) = 0

Elimination the left coefficient

x^{4} (15 x^{2} - 10 x) = 0

Separate the equation into 2 possible cases

x^{4} = 0 15 x^{2} - 10 x = 0

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

x = 0 15 x^{2} - 10 x = 0

Solve the equation

More Steps

x = 0 x = 0 x = \frac{2}{3}

Find the union

x = 0 x = \frac{2}{3}

Check if the solution is in the defined range

x = 0 x = \frac{2}{3}, x \in (- \infty, - \frac{1}{4}) \cup (- \frac{1}{4}, \frac{1}{4}) \cup (\frac{1}{4}, \frac{3 15210}{39}) \cup (\frac{3 15210}{39}, + \infty)

Find the intersection of the solution and the defined range

x = 0 x = \frac{2}{3}

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{6}

Show Solution