Solve for y y+4=5/y

$y + 4 = \frac{5}{y}$

Subtract $4$ from both sides of the equation.

$y = \frac{5}{y} - 4$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, y, 1$

The LCM of one and any expression is the expression.

$y$

Multiply each term in $y = \frac{5}{y} - 4$ by $y$ to eliminate the fractions.

Multiply each term in $y = \frac{5}{y} - 4$ by $y$ .

$y \cdot y = \frac{5}{y} y - 4 y$

Simplify the left side.

Multiply $y$ by $y$ .

$y^{2} = \frac{5}{y} y - 4 y$

Simplify the right side.

Cancel the common factor of $y$ .

Cancel the common factor.

$y^{2} = \frac{5}{y} y - 4 y$

Rewrite the expression.

$y^{2} = 5 - 4 y$

Solve the equation.

Add $4 y$ to both sides of the equation.

$y^{2} + 4 y = 5$

Subtract $5$ from both sides of the equation.

$y^{2} + 4 y - 5 = 0$

Factor $y^{2} + 4 y - 5$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 5$ and whose sum is $4$ .

$- 1, 5$

Write the factored form using these integers.

$(y - 1) (y + 5) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y - 1 = 0$

$y + 5 = 0$

Set $y - 1$ equal to $0$ and solve for $y$ .

Set $y - 1$ equal to $0$ .

$y - 1 = 0$

Add $1$ to both sides of the equation.

$y = 1$

Set $y + 5$ equal to $0$ and solve for $y$ .

Set $y + 5$ equal to $0$ .

$y + 5 = 0$

Subtract $5$ from both sides of the equation.

$y = - 5$

The final solution is all the values that make $(y - 1) (y + 5) = 0$ true.

$y = 1, - 5$

Solve for y y+4=5/y

Related Questions

Support LCMGCF.com by disabling your adblocker.