Solve \left(4y^2 9y-5\right)\:-\left(4y^2-5y^3\right)

Question

Simplify the expression

- \frac{36 y ^{3} - 5}{4 y ^{2} - 5 y ^{3}}

Show Solution

y = 0, y = \frac{4}{5}

Show Solution

y = \frac{3 30}{6}

Alternative Form

y \approx 0.517872

Evaluate

(4 y^{2} \times 9 y - 5) \div (- (4 y^{2} - 5 y^{3}))

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

(4 y^{2} \times 9 y - 5) \div (- (4 y^{2} - 5 y^{3})) = 0

Find the domain

More Steps

(4 y^{2} \times 9 y - 5) \div (- (4 y^{2} - 5 y^{3})) = 0, y \in (- \infty, 0) \cup (0, \frac{4}{5}) \cup (\frac{4}{5}, + \infty)

Calculate

(4 y^{2} \times 9 y - 5) \div (- (4 y^{2} - 5 y^{3})) = 0

Multiply

More Steps

(36 y^{3} - 5) \div (- (4 y^{2} - 5 y^{3})) = 0

Calculate

(36 y^{3} - 5) \div (- 4 y^{2} + 5 y^{3}) = 0

Rewrite the expression

\frac{36 y ^{3} - 5}{- 4 y ^{2} + 5 y ^{3}} = 0

Cross multiply

36 y^{3} - 5 = (- 4 y^{2} + 5 y^{3}) \times 0

Simplify the equation

36 y^{3} - 5 = 0

Move the constant to the right side

36 y^{3} = 5

Divide both sides

\frac{36 y ^{3}}{36} = \frac{5}{36}

Divide the numbers

y^{3} = \frac{5}{36}

Take the 3 -th root on both sides of the equation

3 y^{3} = 3 \frac{5}{36}

Calculate

y = 3 \frac{5}{36}

Simplify the root

More Steps

y = \frac{3 30}{6}

Check if the solution is in the defined range

y = \frac{3 30}{6}, y \in (- \infty, 0) \cup (0, \frac{4}{5}) \cup (\frac{4}{5}, + \infty)

Solution

y = \frac{3 30}{6}

Alternative Form

y \approx 0.517872

Show Solution