Solve (p^3)/(3p-12) (2p-3)/(p-4) p/3

Question

Simplify the expression

\frac{2 p ^{5} - 3 p ^{4}}{9 p ^{2} - 72 p + 144}

Show Solution

p = 4

Show Solution

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

Alternative Form

p_{1} = 0, p_{2} = 1.5

Evaluate

\frac{p ^{3}}{3 p - 12} \times \frac{2 p - 3}{p - 4} \times \frac{p}{3}

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

\frac{p ^{3}}{3 p - 12} \times \frac{2 p - 3}{p - 4} \times \frac{p}{3} = 0

Find the domain

More Steps

\frac{p ^{3}}{3 p - 12} \times \frac{2 p - 3}{p - 4} \times \frac{p}{3} = 0, p \neq = 4

Calculate

\frac{p ^{3}}{3 p - 12} \times \frac{2 p - 3}{p - 4} \times \frac{p}{3} = 0

Multiply the terms

More Steps

\frac{p ^{4} ( 2 p - 3 )}{3 ( 3 p - 12 ) ( p - 4 )} = 0

Cross multiply

p^{4} (2 p - 3) = 3 (3 p - 12) (p - 4) \times 0

Simplify the equation

p^{4} (2 p - 3) = 0

Separate the equation into 2 possible cases

p^{4} = 0 2 p - 3 = 0

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

p = 0 2 p - 3 = 0

Solve the equation

More Steps

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

Check if the solution is in the defined range

p = 0 p = \frac{3}{2}, p \neq = 4

Find the intersection of the solution and the defined range

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

Solution

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

Alternative Form

p_{1} = 0, p_{2} = 1.5

Show Solution