Basic Math Examples

Solve for b 1/b-4=-3/(4b)-2 1/4
Step 1
Simplify the right side.
Tap for more steps...
Step 1.1
Simplify .
Tap for more steps...
Step 1.1.1
Convert to an improper fraction.
Tap for more steps...
Step 1.1.1.1
A mixed number is an addition of its whole and fractional parts.
Step 1.1.1.2
Add and .
Tap for more steps...
Step 1.1.1.2.1
To write as a fraction with a common denominator, multiply by .
Step 1.1.1.2.2
Combine and .
Step 1.1.1.2.3
Combine the numerators over the common denominator.
Step 1.1.1.2.4
Simplify the numerator.
Tap for more steps...
Step 1.1.1.2.4.1
Multiply by .
Step 1.1.1.2.4.2
Add and .
Step 1.1.2
Move the negative in front of the fraction.
Step 2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 2.1
Add to both sides of the equation.
Step 2.2
To write as a fraction with a common denominator, multiply by .
Step 2.3
Combine and .
Step 2.4
Combine the numerators over the common denominator.
Step 2.5
Simplify the numerator.
Tap for more steps...
Step 2.5.1
Multiply by .
Step 2.5.2
Add and .
Step 3
Find the LCD of the terms in the equation.
Tap for more steps...
Step 3.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.2
Since contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
Step 3.3
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 3.4
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 3.5
has factors of and .
Step 3.6
Multiply by .
Step 3.7
The factor for is itself.
occurs time.
Step 3.8
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 3.9
The LCM for is the numeric part multiplied by the variable part.
Step 4
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 4.1
Multiply each term in by .
Step 4.2
Simplify the left side.
Tap for more steps...
Step 4.2.1
Rewrite using the commutative property of multiplication.
Step 4.2.2
Combine and .
Step 4.2.3
Cancel the common factor of .
Tap for more steps...
Step 4.2.3.1
Cancel the common factor.
Step 4.2.3.2
Rewrite the expression.
Step 4.3
Simplify the right side.
Tap for more steps...
Step 4.3.1
Simplify each term.
Tap for more steps...
Step 4.3.1.1
Cancel the common factor of .
Tap for more steps...
Step 4.3.1.1.1
Move the leading negative in into the numerator.
Step 4.3.1.1.2
Cancel the common factor.
Step 4.3.1.1.3
Rewrite the expression.
Step 4.3.1.2
Cancel the common factor of .
Tap for more steps...
Step 4.3.1.2.1
Factor out of .
Step 4.3.1.2.2
Cancel the common factor.
Step 4.3.1.2.3
Rewrite the expression.
Step 5
Solve the equation.
Tap for more steps...
Step 5.1
Rewrite the equation as .
Step 5.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 5.2.1
Add to both sides of the equation.
Step 5.2.2
Add and .
Step 5.3
Divide each term in by and simplify.
Tap for more steps...
Step 5.3.1
Divide each term in by .
Step 5.3.2
Simplify the left side.
Tap for more steps...
Step 5.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.3.2.1.1
Cancel the common factor.
Step 5.3.2.1.2
Divide by .
Step 5.3.3
Simplify the right side.
Tap for more steps...
Step 5.3.3.1
Divide by .