Algebra Examples

$\frac{1}{1 - x^{2}} = - | 3 x - 2 | + 5$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $1$ as $1^{2}$ .

$\frac{1}{1^{2} - x^{2}} = - | 3 x - 2 | + 5$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

$\frac{1}{(1 + x) (1 - x)} = - | 3 x - 2 | + 5$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 1.37466105, - 0.53382185, 0.87803835, 2.40314015$

Step 3