Finite Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Factor $x^{4} (x + 3)$ out of $5 x^{4} {(x + 3)}^{2} - 2 x^{5} (x + 3)$ .

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Step 1.1.1

Factor $x^{4} (x + 3)$ out of $5 x^{4} {(x + 3)}^{2}$ .

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

Step 1.1.2

Factor $x^{4} (x + 3)$ out of $- 2 x^{5} (x + 3)$ .

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

Step 1.1.3

Factor $x^{4} (x + 3)$ out of $x^{4} (x + 3) (5 (x + 3)) + x^{4} (x + 3) (- 2 x)$ .

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Multiply $5$ by $3$ .

$\frac{x^{4} (x + 3) (5 x + 15 - 2 x)}{{(x + 3)}^{4}}$

Step 1.4

Subtract $2 x$ from $5 x$ .

$\frac{x^{4} (x + 3) (3 x + 15)}{{(x + 3)}^{4}}$

Step 1.5

Factor $3$ out of $3 x + 15$ .

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Step 1.5.1

Factor $3$ out of $3 x$ .

$\frac{x^{4} (x + 3) (3 (x) + 15)}{{(x + 3)}^{4}}$

Step 1.5.2

Factor $3$ out of $15$ .

$\frac{x^{4} (x + 3) (3 x + 3 \cdot 5)}{{(x + 3)}^{4}}$

Step 1.5.3

Factor $3$ out of $3 x + 3 \cdot 5$ .

$\frac{x^{4} (x + 3) (3 (x + 5))}{{(x + 3)}^{4}}$

$\frac{x^{4} (x + 3) \cdot 3 (x + 5)}{{(x + 3)}^{4}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $x + 3$ and ${(x + 3)}^{4}$ .

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Step 2.1.1

Factor $x + 3$ out of $x^{4} (x + 3) \cdot 3 (x + 5)$ .

$\frac{(x + 3) (x^{4} \cdot 3 (x + 5))}{{(x + 3)}^{4}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $x + 3$ out of ${(x + 3)}^{4}$ .

$\frac{(x + 3) (x^{4} \cdot 3 (x + 5))}{(x + 3) {(x + 3)}^{3}}$

Step 2.1.2.2

Cancel the common factor.

$\frac{(x + 3) (x^{4} \cdot 3 (x + 5))}{(x + 3) {(x + 3)}^{3}}$

Step 2.1.2.3

Rewrite the expression.

$\frac{x^{4} \cdot 3 (x + 5)}{{(x + 3)}^{3}}$

Step 2.2

Move $3$ to the left of $x^{4}$ .

$\frac{3 x^{4} (x + 5)}{{(x + 3)}^{3}}$