Basic Math Examples

$\frac{z^{2}}{z - 6} + \frac{z - 42}{z - 6}$

Step 1

Combine the numerators over the common denominator.

$\frac{z^{2} + z - 42}{z - 6}$

Step 2

Factor $z^{2} + z - 42$ using the AC method.

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Step 2.1

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 $- 42$ and whose sum is $1$ .

$- 6, 7$

Step 2.2

Write the factored form using these integers.

$\frac{(z - 6) (z + 7)}{z - 6}$

Step 3

Cancel the common factor of $z - 6$ .

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Step 3.1

Cancel the common factor.

$\frac{(z - 6) (z + 7)}{z - 6}$

Step 3.2

Divide $z + 7$ by $1$ .

$z + 7$