Finite Math Examples

Simplify (6x)/(7x^2-6x-16)-(5x)/(7x^2-15+2)
Step 1
Simplify each term.
Tap for more steps...
Step 1.1
Factor by grouping.
Tap for more steps...
Step 1.1.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps...
Step 1.1.1.1
Factor out of .
Step 1.1.1.2
Rewrite as plus
Step 1.1.1.3
Apply the distributive property.
Step 1.1.2
Factor out the greatest common factor from each group.
Tap for more steps...
Step 1.1.2.1
Group the first two terms and the last two terms.
Step 1.1.2.2
Factor out the greatest common factor (GCF) from each group.
Step 1.1.3
Factor the polynomial by factoring out the greatest common factor, .
Step 1.2
Add and .
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps...
Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 4.3
Reorder the factors of .
Step 4.4
Reorder the factors of .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify the numerator.
Tap for more steps...
Step 6.1
Factor out of .
Tap for more steps...
Step 6.1.1
Factor out of .
Step 6.1.2
Factor out of .
Step 6.1.3
Factor out of .
Step 6.2
Apply the distributive property.
Step 6.3
Multiply by .
Step 6.4
Multiply by .
Step 6.5
Expand using the FOIL Method.
Tap for more steps...
Step 6.5.1
Apply the distributive property.
Step 6.5.2
Apply the distributive property.
Step 6.5.3
Apply the distributive property.
Step 6.6
Simplify and combine like terms.
Tap for more steps...
Step 6.6.1
Simplify each term.
Tap for more steps...
Step 6.6.1.1
Multiply by by adding the exponents.
Tap for more steps...
Step 6.6.1.1.1
Move .
Step 6.6.1.1.2
Multiply by .
Step 6.6.1.2
Multiply by .
Step 6.6.1.3
Multiply by .
Step 6.6.2
Add and .
Step 6.7
Apply the distributive property.
Step 6.8
Simplify.
Tap for more steps...
Step 6.8.1
Multiply by .
Step 6.8.2
Multiply by .
Step 6.8.3
Multiply by .
Step 6.9
Subtract from .
Step 6.10
Add and .