Pre-Algebra Examples

$x + 5 \div x^{3} + 1 x^{2} - 10 x + 54$

Step 1

Write $x + 5 \div x^{3} + 1 x^{2} - 10 x + 54$ as an equation.

$y = x + 5 \div x^{3} + 1 x^{2} - 10 x + 54$

Step 2

Simplify $x + 5 \div x^{3} + 1 x^{2} - 10 x + 54$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite the division as a fraction.

$y = x + \frac{5}{x^{3}} + 1 x^{2} - 10 x + 54$

Step 2.1.2

Multiply $x^{2}$ by $1$ .

$y = x + \frac{5}{x^{3}} + x^{2} - 10 x + 54$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $10 x$ from $x$ .

$y = - 9 x + \frac{5}{x^{3}} + x^{2} + 54$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Move $\frac{5}{x^{3}}$ .

$y = - 9 x + x^{2} + \frac{5}{x^{3}} + 54$

Step 2.2.2.2

Reorder $- 9 x$ and $x^{2}$ .

$y = x^{2} - 9 x + \frac{5}{x^{3}} + 54$

Step 3

The given equation $y = x^{2} - 9 x + \frac{5}{x^{3}} + 54$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$