Basic Math Examples

$\frac{x}{4 - 9 x} + \frac{7 x}{9 x - 4}$

Step 1

Simplify terms.

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Step 1.1

Factor $- 1$ out of $9 x$ .

$\frac{x}{4 - 9 x} + \frac{7 x}{- (- 9 x) - 4}$

Step 1.2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{x}{4 - 9 x} + \frac{7 x}{- (- 9 x) - 1 (4)}$

Step 1.3

Factor $- 1$ out of $- (- 9 x) - 1 (4)$ .

$\frac{x}{4 - 9 x} + \frac{7 x}{- (- 9 x + 4)}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Move a negative from the denominator of $\frac{7 x}{- (- 9 x + 4)}$ to the numerator.

$\frac{x}{4 - 9 x} + \frac{- (7 x)}{- 9 x + 4}$

Step 1.4.2

Reorder terms.

$\frac{x}{- 9 x + 4} + \frac{- (7 x)}{- 9 x + 4}$

$\frac{x}{- 9 x + 4} + \frac{- (7 x)}{- 9 x + 4}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x - (7 x)}{- 9 x + 4}$

$\frac{x - (7 x)}{- 9 x + 4}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $x$ out of $x - 1 \cdot 7 x$ .

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Step 2.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - 1 \cdot 7 x}{- 9 x + 4}$

Step 2.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - 1 \cdot 7 x}{- 9 x + 4}$

Step 2.1.3

Factor $x$ out of $- 1 \cdot 7 x$ .

$\frac{x \cdot 1 + x (- 1 \cdot 7)}{- 9 x + 4}$

Step 2.1.4

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 7)$ .

$\frac{x (1 - 1 \cdot 7)}{- 9 x + 4}$

$\frac{x (1 - 1 \cdot 7)}{- 9 x + 4}$

Step 2.2

Multiply $- 1$ by $7$ .

$\frac{x (1 - 7)}{- 9 x + 4}$

Step 2.3

Subtract $7$ from $1$ .

$\frac{x \cdot - 6}{- 9 x + 4}$

$\frac{x \cdot - 6}{- 9 x + 4}$

Step 3

Simplify with factoring out.

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Step 3.1

Move $- 6$ to the left of $x$ .

$\frac{- 6 \cdot x}{- 9 x + 4}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{6 \cdot x}{- 9 x + 4}$

Step 3.3

Factor $- 1$ out of $- 9 x$ .

$- \frac{6 x}{- (9 x) + 4}$

Step 3.4

Rewrite $4$ as $- 1 (- 4)$ .

$- \frac{6 x}{- (9 x) - 1 (- 4)}$

Step 3.5

Factor $- 1$ out of $- (9 x) - 1 (- 4)$ .

$- \frac{6 x}{- (9 x - 4)}$

Step 3.6

Simplify the expression.

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Step 3.6.1

Rewrite $- (9 x - 4)$ as $- 1 (9 x - 4)$ .

$- \frac{6 x}{- 1 (9 x - 4)}$

Step 3.6.2

Move the negative in front of the fraction.

$- - \frac{6 x}{9 x - 4}$

Step 3.6.3

Multiply $- 1$ by $- 1$ .

$1 \frac{6 x}{9 x - 4}$

Step 3.6.4

Multiply $\frac{6 x}{9 x - 4}$ by $1$ .

$\frac{6 x}{9 x - 4}$

$\frac{6 x}{9 x - 4}$

$\frac{6 x}{9 x - 4}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$