Calculus Examples

Simplify (x/(x-3))+(x-21)/(x^2-9)
Step 1
Simplify the denominator.
Tap for more steps...
Step 1.1
Rewrite as .
Step 1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps...
Step 3.1
Multiply by .
Step 3.2
Reorder the factors of .
Step 4
Combine the numerators over the common denominator.
Step 5
Simplify the numerator.
Tap for more steps...
Step 5.1
Apply the distributive property.
Step 5.2
Multiply by .
Step 5.3
Move to the left of .
Step 5.4
Add and .
Step 5.5
Factor using the AC method.
Tap for more steps...
Step 5.5.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 5.5.2
Write the factored form using these integers.
Step 6
Cancel the common factor of .
Tap for more steps...
Step 6.1
Cancel the common factor.
Step 6.2
Rewrite the expression.