Finite Math Examples

$\frac{x}{1} + \frac{4}{x} = 5$

Step 1

Divide $x$ by $1$ .

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

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

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

$1, x, 1$

Step 2.2

The LCM of one and any expression is the expression.

$x$

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify each term.

Tap for more steps...

Step 3.2.1.1

Multiply $x$ by $x$ .

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

Step 3.2.1.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.2.1.2.1

Cancel the common factor.

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

Step 3.2.1.2.2

Rewrite the expression.

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

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

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

Step 4.2

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

Tap for more steps...

Step 4.2.1

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 $- 5$ .

$- 4, - 1$

Step 4.2.2

Write the factored form using these integers.

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

Step 4.3

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

$x - 4 = 0$

$x - 1 = 0$

Step 4.4

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

Tap for more steps...

Step 4.4.1

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

$x - 4 = 0$

Step 4.4.2

Add $4$ to both sides of the equation.

$x = 4$

Step 4.5

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

Tap for more steps...

Step 4.5.1

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

$x - 1 = 0$

Step 4.5.2

Add $1$ to both sides of the equation.

$x = 1$

Step 4.6

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

$x = 4, 1$