Basic Math Examples

$\frac{4 c - 11}{c^{2} - 13 c + 42} + \frac{4 - 3 c}{c^{2} - 13 c + 42}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{4 c - 11 + 4 - 3 c}{c^{2} - 13 c + 42}$

Step 1.2

Subtract $3 c$ from $4 c$ .

$\frac{c - 11 + 4}{c^{2} - 13 c + 42}$

Step 1.3

Add $- 11$ and $4$ .

$\frac{c - 7}{c^{2} - 13 c + 42}$

Step 2

Factor $c^{2} - 13 c + 42$ 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 $- 13$ .

$- 7, - 6$

Step 2.2

Write the factored form using these integers.

$\frac{c - 7}{(c - 7) (c - 6)}$

Step 3

Cancel the common factor of $c - 7$ .

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Step 3.1

Cancel the common factor.

$\frac{c - 7}{(c - 7) (c - 6)}$

Step 3.2

Rewrite the expression.

$\frac{1}{c - 6}$