Solve for x 4/x+x=5

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

Step 1

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.

$x, 1, 1$

The LCM of one and any expression is the expression.

$x$

Step 2

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

Multiply each term in $\frac{4}{x} + x = 5$ by $x$ .

$\frac{4}{x} x + x \cdot x = 5 x$

Simplify the left side.

Simplify each term.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{4}{x} x + x \cdot x = 5 x$

Rewrite the expression.

$4 + x \cdot x = 5 x$

Multiply $x$ by $x$ .

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

Step 3

Solve the equation.

Subtract $5 x$ from both sides of the equation.

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

Factor $4 + x^{2} - 5 x$ 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 $4$ and whose sum is $- 5$ .

$- 4, - 1$

Write the factored form using these integers.

$(x - 4) (x - 1) = 0$

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

$x - 4 = 0$

$x - 1 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $(x - 4) (x - 1) = 0$ true.

$x = 4, 1$

Solve for x 4/x+x=5

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