Finite Math Examples

$\frac{5 x + 5 \cdot (2 x^{2}) + x - 3}{7 x - 7 x^{2} \cdot (4 x^{2}) - 9}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $5$ by $2$ .

$\frac{5 x + 10 x^{2} + x - 3}{7 x - 7 x^{2} \cdot (4 x^{2}) - 9}$

Step 1.2

Add $5 x$ and $x$ .

$\frac{10 x^{2} + 6 x - 3}{7 x - 7 x^{2} \cdot (4 x^{2}) - 9}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite using the commutative property of multiplication.

$\frac{10 x^{2} + 6 x - 3}{7 x - 7 \cdot 4 x^{2} x^{2} - 9}$

Step 2.2

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 2.2.1

Move $x^{2}$ .

$\frac{10 x^{2} + 6 x - 3}{7 x - 7 \cdot 4 (x^{2} x^{2}) - 9}$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10 x^{2} + 6 x - 3}{7 x - 7 \cdot 4 x^{2 + 2} - 9}$

Step 2.2.3

Add $2$ and $2$ .

$\frac{10 x^{2} + 6 x - 3}{7 x - 7 \cdot 4 x^{4} - 9}$

Step 2.3

Multiply $- 7$ by $4$ .

$\frac{10 x^{2} + 6 x - 3}{7 x - 28 x^{4} - 9}$

Step 2.4

Reorder terms.

$\frac{10 x^{2} + 6 x - 3}{- 28 x^{4} + 7 x - 9}$

Step 3

Simplify with factoring out.

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Step 3.1

Factor $- 1$ out of $- 28 x^{4}$ .

$\frac{10 x^{2} + 6 x - 3}{- (28 x^{4}) + 7 x - 9}$

Step 3.2

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

$\frac{10 x^{2} + 6 x - 3}{- (28 x^{4}) - (- 7 x) - 9}$

Step 3.3

Factor $- 1$ out of $- (28 x^{4}) - (- 7 x)$ .

$\frac{10 x^{2} + 6 x - 3}{- (28 x^{4} - 7 x) - 9}$

Step 3.4

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

$\frac{10 x^{2} + 6 x - 3}{- (28 x^{4} - 7 x) - 1 (9)}$

Step 3.5

Factor $- 1$ out of $- (28 x^{4} - 7 x) - 1 (9)$ .

$\frac{10 x^{2} + 6 x - 3}{- (28 x^{4} - 7 x + 9)}$

Step 3.6

Rewrite negatives.

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Step 3.6.1

Rewrite $- (28 x^{4} - 7 x + 9)$ as $- 1 (28 x^{4} - 7 x + 9)$ .

$\frac{10 x^{2} + 6 x - 3}{- 1 (28 x^{4} - 7 x + 9)}$

Step 3.6.2

Move the negative in front of the fraction.

$- \frac{10 x^{2} + 6 x - 3}{28 x^{4} - 7 x + 9}$