Algebra Examples

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

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

Step 1

Factor

x^{2} + x - 12

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

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Step 1.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

- 12

$- 12$ and whose sum is

1

$1$ .

- 3, 4

$- 3, 4$

Step 1.2

Write the factored form using these integers.

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

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

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

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

Step 2

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

x \approx 2.53397976

$x \approx 2.53397976$

Step 3