Basic Math Examples

$\frac{4 v - 7}{v^{2} - 9 v + 18} + \frac{4 - 3 v}{v^{2} - 9 v + 18}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{4 v - 7 + 4 - 3 v}{v^{2} - 9 v + 18}$

Step 1.2

Subtract $3 v$ from $4 v$ .

$\frac{v - 7 + 4}{v^{2} - 9 v + 18}$

Step 1.3

Add $- 7$ and $4$ .

$\frac{v - 3}{v^{2} - 9 v + 18}$

Step 2

Factor $v^{2} - 9 v + 18$ 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 $18$ and whose sum is $- 9$ .

$- 6, - 3$

Step 2.2

Write the factored form using these integers.

$\frac{v - 3}{(v - 6) (v - 3)}$

Step 3

Cancel the common factor of $v - 3$ .

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Step 3.1

Cancel the common factor.

$\frac{v - 3}{(v - 6) (v - 3)}$

Step 3.2

Rewrite the expression.

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