Precalculus Examples

Solve for y (4y^2-8y+12)/(y^2+y-6)=3
Step 1
Factor each term.
Tap for more steps...
Step 1.1
Factor out of .
Tap for more steps...
Step 1.1.1
Factor out of .
Step 1.1.2
Factor out of .
Step 1.1.3
Factor out of .
Step 1.1.4
Factor out of .
Step 1.1.5
Factor out of .
Step 1.2
Factor using the AC method.
Tap for more steps...
Step 1.2.1
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 1.2.2
Write the factored form using these integers.
Step 2
Find the LCD of the terms in the equation.
Tap for more steps...
Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
The LCM of one and any expression is the expression.
Step 3
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
Tap for more steps...
Step 3.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Rewrite the expression.
Step 3.2.2
Apply the distributive property.
Step 3.2.3
Simplify.
Tap for more steps...
Step 3.2.3.1
Multiply by .
Step 3.2.3.2
Multiply by .
Step 3.3
Simplify the right side.
Tap for more steps...
Step 3.3.1
Expand using the FOIL Method.
Tap for more steps...
Step 3.3.1.1
Apply the distributive property.
Step 3.3.1.2
Apply the distributive property.
Step 3.3.1.3
Apply the distributive property.
Step 3.3.2
Simplify and combine like terms.
Tap for more steps...
Step 3.3.2.1
Simplify each term.
Tap for more steps...
Step 3.3.2.1.1
Multiply by .
Step 3.3.2.1.2
Move to the left of .
Step 3.3.2.1.3
Multiply by .
Step 3.3.2.2
Subtract from .
Step 3.3.3
Apply the distributive property.
Step 3.3.4
Multiply by .
Step 4
Solve the equation.
Tap for more steps...
Step 4.1
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from both sides of the equation.
Step 4.1.3
Subtract from .
Step 4.1.4
Subtract from .
Step 4.2
Add to both sides of the equation.
Step 4.3
Add and .
Step 4.4
Factor using the AC method.
Tap for more steps...
Step 4.4.1
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 4.4.2
Write the factored form using these integers.
Step 4.5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.6
Set equal to and solve for .
Tap for more steps...
Step 4.6.1
Set equal to .
Step 4.6.2
Add to both sides of the equation.
Step 4.7
Set equal to and solve for .
Tap for more steps...
Step 4.7.1
Set equal to .
Step 4.7.2
Add to both sides of the equation.
Step 4.8
The final solution is all the values that make true.