Solve y-6/y=5 - ScanMath

Question

Solve the equation

y_{1} = - 1, y_{2} = 6

Evaluate

y - \frac{6}{y} = 5

Find the domain

y - \frac{6}{y} = 5, y \neq = 0

Multiply both sides of the equation by LCD

(y - \frac{6}{y}) y = 5 y

Simplify the equation

More Steps

Evaluate

(y - \frac{6}{y}) y

Apply the distributive property

y \times y - \frac{6}{y} \times y

Simplify

y \times y - 6

Multiply the terms

y^{2} - 6

y^{2} - 6 = 5 y

Move the expression to the left side

y^{2} - 6 - 5 y = 0

Factor the expression

More Steps

Evaluate

y^{2} - 6 - 5 y

Reorder the terms

y^{2} - 5 y - 6

Rewrite the expression

y^{2} + (1 - 6) y - 6

Calculate

y^{2} + y - 6 y - 6

Rewrite the expression

y \times y + y - 6 y - 6

Factor out y from the expression

y (y + 1) - 6 y - 6

Factor out - 6 from the expression

y (y + 1) - 6 (y + 1)

Factor out y + 1 from the expression

(y - 6) (y + 1)

(y - 6) (y + 1) = 0

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

y - 6 = 0 y + 1 = 0

Solve the equation for y

More Steps

Evaluate

y - 6 = 0

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

y = 0 + 6

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

y = 6

y = 6 y + 1 = 0

Solve the equation for y

More Steps

Evaluate

y + 1 = 0

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

y = 0 - 1

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

y = - 1

y = 6 y = - 1

Check if the solution is in the defined range

y = 6 y = - 1, y \neq = 0

Find the intersection of the solution and the defined range

y = 6 y = - 1

Solution

y_{1} = - 1, y_{2} = 6

Show Solution