Algebra Examples

x^{2} + 2 + \frac{1}{x^{2}}

$x^{2} + 2 + \frac{1}{x^{2}}$

Step 1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

x^{2} + 2 + \frac{1^{2}}{x^{2}}

$x^{2} + 2 + \frac{1^{2}}{x^{2}}$

Step 2

Rewrite

\frac{1^{2}}{x^{2}}

$\frac{1^{2}}{x^{2}}$ as

{(\frac{1}{x})}^{2}

${(\frac{1}{x})}^{2}$ .

x^{2} + 2 + {(\frac{1}{x})}^{2}

$x^{2} + 2 + {(\frac{1}{x})}^{2}$

Step 3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

2 = 2 \cdot x \cdot \frac{1}{x}

$2 = 2 \cdot x \cdot \frac{1}{x}$

Step 4

Rewrite the polynomial.

x^{2} + 2 \cdot x \cdot \frac{1}{x} + {(\frac{1}{x})}^{2}

$x^{2} + 2 \cdot x \cdot \frac{1}{x} + {(\frac{1}{x})}^{2}$

Step 5

Factor using the perfect square trinomial rule

a^{2} + 2 a b + b^{2} = {(a + b)}^{2}

$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where

a = x

$a = x$ and

b = \frac{1}{x}

$b = \frac{1}{x}$ .

{(x + \frac{1}{x})}^{2}

${(x + \frac{1}{x})}^{2}$