Trigonometry Examples

Solve for x 2/(z-1)-2/3=4/(z+1)
Step 1
Add to both sides of the equation.
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 is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Step 2.3
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.4
Since has no factors besides and .
is a prime number
Step 2.5
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.6
The factor for is itself.
occurs time.
Step 2.7
The factor for is itself.
occurs time.
Step 2.8
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 2.9
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
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
Rewrite using the commutative property of multiplication.
Step 3.2.2
Multiply .
Tap for more steps...
Step 3.2.2.1
Combine and .
Step 3.2.2.2
Multiply by .
Step 3.2.3
Cancel the common factor of .
Tap for more steps...
Step 3.2.3.1
Cancel the common factor.
Step 3.2.3.2
Rewrite the expression.
Step 3.2.4
Apply the distributive property.
Step 3.2.5
Multiply by .
Step 3.3
Simplify the right side.
Tap for more steps...
Step 3.3.1
Simplify each term.
Tap for more steps...
Step 3.3.1.1
Rewrite using the commutative property of multiplication.
Step 3.3.1.2
Multiply .
Tap for more steps...
Step 3.3.1.2.1
Combine and .
Step 3.3.1.2.2
Multiply by .
Step 3.3.1.3
Cancel the common factor of .
Tap for more steps...
Step 3.3.1.3.1
Factor out of .
Step 3.3.1.3.2
Cancel the common factor.
Step 3.3.1.3.3
Rewrite the expression.
Step 3.3.1.4
Apply the distributive property.
Step 3.3.1.5
Multiply by .
Step 3.3.1.6
Cancel the common factor of .
Tap for more steps...
Step 3.3.1.6.1
Factor out of .
Step 3.3.1.6.2
Cancel the common factor.
Step 3.3.1.6.3
Rewrite the expression.
Step 3.3.1.7
Expand using the FOIL Method.
Tap for more steps...
Step 3.3.1.7.1
Apply the distributive property.
Step 3.3.1.7.2
Apply the distributive property.
Step 3.3.1.7.3
Apply the distributive property.
Step 3.3.1.8
Combine the opposite terms in .
Tap for more steps...
Step 3.3.1.8.1
Reorder the factors in the terms and .
Step 3.3.1.8.2
Subtract from .
Step 3.3.1.8.3
Add and .
Step 3.3.1.9
Simplify each term.
Tap for more steps...
Step 3.3.1.9.1
Multiply by .
Step 3.3.1.9.2
Multiply by .
Step 3.3.1.10
Apply the distributive property.
Step 3.3.1.11
Multiply by .
Step 3.3.2
Subtract from .
Step 4
Solve the equation.
Tap for more steps...
Step 4.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.2
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Subtract from .
Step 4.3
Subtract from both sides of the equation.
Step 4.4
Subtract from .
Step 4.5
Factor the left side of the equation.
Tap for more steps...
Step 4.5.1
Factor out of .
Tap for more steps...
Step 4.5.1.1
Factor out of .
Step 4.5.1.2
Factor out of .
Step 4.5.1.3
Factor out of .
Step 4.5.1.4
Factor out of .
Step 4.5.1.5
Factor out of .
Step 4.5.2
Let . Substitute for all occurrences of .
Step 4.5.3
Factor using the AC method.
Tap for more steps...
Step 4.5.3.1
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 4.5.3.2
Write the factored form using these integers.
Step 4.5.4
Factor.
Tap for more steps...
Step 4.5.4.1
Replace all occurrences of with .
Step 4.5.4.2
Remove unnecessary parentheses.
Step 4.6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
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
Set equal to and solve for .
Tap for more steps...
Step 4.8.1
Set equal to .
Step 4.8.2
Subtract from both sides of the equation.
Step 4.9
The final solution is all the values that make true.