Algebra Examples

$\frac{x^{2} + x - 12}{x - 5} = \frac{2 x + 3}{x + 4}$

Step 1

Factor $x^{2} + x - 12$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 12$ and whose sum is $1$ .

$- 3, 4$

Step 1.2

Write the factored form using these integers.

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

Step 2

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

$x \approx 2.53397976$

Step 3