Basic Math Examples

Solve for r 103.7=(1/(1+r))*30.4/r
Step 1
Rewrite the equation as .
Step 2
Factor each term.
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Step 2.1
Multiply by .
Step 2.2
Multiply by .
Step 3
Find the LCD of the terms in the equation.
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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
The LCM of one and any expression is the expression.
Step 4
Multiply each term in by to eliminate the fractions.
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Step 4.1
Multiply each term in by .
Step 4.2
Simplify the left side.
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Step 4.2.1
Cancel the common factor of .
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Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
Rewrite the expression.
Step 4.3
Simplify the right side.
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Step 4.3.1
Apply the distributive property.
Step 4.3.2
Simplify the expression.
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Step 4.3.2.1
Multiply by .
Step 4.3.2.2
Multiply by .
Step 4.3.3
Apply the distributive property.
Step 5
Solve the equation.
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Step 5.1
Rewrite the equation as .
Step 5.2
Subtract from both sides of the equation.
Step 5.3
Factor the left side of the equation.
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Step 5.3.1
Factor out of .
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Step 5.3.1.1
Factor out of .
Step 5.3.1.2
Factor out of .
Step 5.3.1.3
Factor out of .
Step 5.3.1.4
Factor out of .
Step 5.3.1.5
Factor out of .
Step 5.3.2
Reorder terms.
Step 5.4
Divide each term in by and simplify.
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Step 5.4.1
Divide each term in by .
Step 5.4.2
Simplify the left side.
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Step 5.4.2.1
Cancel the common factor of .
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Step 5.4.2.1.1
Cancel the common factor.
Step 5.4.2.1.2
Divide by .
Step 5.4.3
Simplify the right side.
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Step 5.4.3.1
Divide by .
Step 5.5
Use the quadratic formula to find the solutions.
Step 5.6
Substitute the values , , and into the quadratic formula and solve for .
Step 5.7
Simplify.
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Step 5.7.1
Simplify the numerator.
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Step 5.7.1.1
Raise to the power of .
Step 5.7.1.2
Multiply .
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Step 5.7.1.2.1
Multiply by .
Step 5.7.1.2.2
Multiply by .
Step 5.7.1.3
Add and .
Step 5.7.2
Multiply by .
Step 5.8
The final answer is the combination of both solutions.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: