Pre-Algebra Examples

Solve for x 4/(3+x)+3/(2x+1)=1
Step 1
Find the LCD of the terms in the equation.
Tap for more steps...
Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
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 1.3
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.4
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 1.5
The factor for is itself.
occurs time.
Step 1.6
The factor for is itself.
occurs time.
Step 1.7
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 2
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
Tap for more steps...
Step 2.2.1
Simplify each term.
Tap for more steps...
Step 2.2.1.1
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.1.1
Cancel the common factor.
Step 2.2.1.1.2
Rewrite the expression.
Step 2.2.1.2
Apply the distributive property.
Step 2.2.1.3
Multiply by .
Step 2.2.1.4
Multiply by .
Step 2.2.1.5
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.5.1
Factor out of .
Step 2.2.1.5.2
Cancel the common factor.
Step 2.2.1.5.3
Rewrite the expression.
Step 2.2.1.6
Apply the distributive property.
Step 2.2.1.7
Multiply by .
Step 2.2.2
Simplify by adding terms.
Tap for more steps...
Step 2.2.2.1
Add and .
Step 2.2.2.2
Add and .
Step 2.3
Simplify the right side.
Tap for more steps...
Step 2.3.1
Multiply by .
Step 2.3.2
Expand using the FOIL Method.
Tap for more steps...
Step 2.3.2.1
Apply the distributive property.
Step 2.3.2.2
Apply the distributive property.
Step 2.3.2.3
Apply the distributive property.
Step 2.3.3
Simplify and combine like terms.
Tap for more steps...
Step 2.3.3.1
Simplify each term.
Tap for more steps...
Step 2.3.3.1.1
Multiply by .
Step 2.3.3.1.2
Multiply by .
Step 2.3.3.1.3
Rewrite using the commutative property of multiplication.
Step 2.3.3.1.4
Multiply by by adding the exponents.
Tap for more steps...
Step 2.3.3.1.4.1
Move .
Step 2.3.3.1.4.2
Multiply by .
Step 2.3.3.1.5
Multiply by .
Step 2.3.3.2
Add and .
Step 3
Solve the equation.
Tap for more steps...
Step 3.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 3.2
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from .
Step 3.3
Subtract from both sides of the equation.
Step 3.4
Subtract from .
Step 3.5
Factor the left side of the equation.
Tap for more steps...
Step 3.5.1
Factor out of .
Tap for more steps...
Step 3.5.1.1
Factor out of .
Step 3.5.1.2
Factor out of .
Step 3.5.1.3
Factor out of .
Step 3.5.1.4
Factor out of .
Step 3.5.1.5
Factor out of .
Step 3.5.2
Reorder terms.
Step 3.6
Divide each term in by and simplify.
Tap for more steps...
Step 3.6.1
Divide each term in by .
Step 3.6.2
Simplify the left side.
Tap for more steps...
Step 3.6.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.6.2.1.1
Cancel the common factor.
Step 3.6.2.1.2
Divide by .
Step 3.6.3
Simplify the right side.
Tap for more steps...
Step 3.6.3.1
Divide by .
Step 3.7
Use the quadratic formula to find the solutions.
Step 3.8
Substitute the values , , and into the quadratic formula and solve for .
Step 3.9
Simplify.
Tap for more steps...
Step 3.9.1
Simplify the numerator.
Tap for more steps...
Step 3.9.1.1
Raise to the power of .
Step 3.9.1.2
Multiply .
Tap for more steps...
Step 3.9.1.2.1
Multiply by .
Step 3.9.1.2.2
Multiply by .
Step 3.9.1.3
Add and .
Step 3.9.1.4
Rewrite as .
Tap for more steps...
Step 3.9.1.4.1
Factor out of .
Step 3.9.1.4.2
Rewrite as .
Step 3.9.1.5
Pull terms out from under the radical.
Step 3.9.2
Multiply by .
Step 3.9.3
Simplify .
Step 3.10
The final answer is the combination of both solutions.
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: