Solve (5y^2 - 6y 7) / (5y - 1)

Question

Simplify the expression

Solution

\frac{5 y ^{2} - 42 y}{5 y - 1}

Evaluate

\frac{5 y ^{2} - 6 y \times 7}{5 y - 1}

Solution

\frac{5 y ^{2} - 42 y}{5 y - 1}

Show Solution

Find the excluded values

y = \frac{1}{5}

Evaluate

\frac{5 y ^{2} - 6 y \times 7}{5 y - 1}

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

5 y - 1 = 0

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

5 y = 0 + 1

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

5 y = 1

Divide both sides

\frac{5 y}{5} = \frac{1}{5}

Solution

y = \frac{1}{5}

Show Solution

Find the roots

Find the roots of the algebra expression

y_{1} = 0, y_{2} = \frac{42}{5}

Alternative Form

y_{1} = 0, y_{2} = 8.4

Evaluate

\frac{5 y ^{2} - 6 y \times 7}{5 y - 1}

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

\frac{5 y ^{2} - 6 y \times 7}{5 y - 1} = 0

Find the domain

More Steps

Evaluate

5 y - 1 \neq = 0

Move the constant to the right side

5 y \neq = 0 + 1

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

5 y \neq = 1

Divide both sides

\frac{5 y}{5} \neq = \frac{1}{5}

Divide the numbers

y \neq = \frac{1}{5}

\frac{5 y ^{2} - 6 y \times 7}{5 y - 1} = 0, y \neq = \frac{1}{5}

Calculate

\frac{5 y ^{2} - 6 y \times 7}{5 y - 1} = 0

Multiply the terms

\frac{5 y ^{2} - 42 y}{5 y - 1} = 0

Cross multiply

5 y^{2} - 42 y = (5 y - 1) \times 0

Simplify the equation

5 y^{2} - 42 y = 0

Factor the expression

More Steps

Evaluate

5 y^{2} - 42 y

Rewrite the expression

y \times 5 y - y \times 42

Factor out y from the expression

y (5 y - 42)

y (5 y - 42) = 0

When the product of factors equals 0,at least one factor is 0

y = 0 5 y - 42 = 0

Solve the equation for y

More Steps

Evaluate

5 y - 42 = 0

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

5 y = 0 + 42

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

5 y = 42

Divide both sides

\frac{5 y}{5} = \frac{42}{5}

Divide the numbers

y = \frac{42}{5}

y = 0 y = \frac{42}{5}

Check if the solution is in the defined range

y = 0 y = \frac{42}{5}, y \neq = \frac{1}{5}

Find the intersection of the solution and the defined range

y = 0 y = \frac{42}{5}

Solution

y_{1} = 0, y_{2} = \frac{42}{5}

Alternative Form

y_{1} = 0, y_{2} = 8.4

Show Solution

(5y^2 6y 7) / (5y 1)

Simplify the expression

Find the excluded values

Find the roots