Basic Math Examples

Solve for a a/(a-1)=-1/(a+1)
aa-1=-1a+1aa1=1a+1
Step 1
Move the negative in front of the fraction.
aa-1=-1a+1aa1=1a+1
Step 2
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
a(a+1)=(a-1)-1a(a+1)=(a1)1
Step 3
Solve the equation for aa.
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Step 3.1
Simplify a(a+1)a(a+1).
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Step 3.1.1
Rewrite.
0+0+a(a+1)=(a-1)-10+0+a(a+1)=(a1)1
Step 3.1.2
Simplify by adding zeros.
a(a+1)=(a-1)-1a(a+1)=(a1)1
Step 3.1.3
Apply the distributive property.
aa+a1=(a-1)-1aa+a1=(a1)1
Step 3.1.4
Simplify the expression.
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Step 3.1.4.1
Multiply aa by aa.
a2+a1=(a-1)-1a2+a1=(a1)1
Step 3.1.4.2
Multiply aa by 11.
a2+a=(a-1)-1a2+a=(a1)1
a2+a=(a-1)-1a2+a=(a1)1
a2+a=(a-1)-1a2+a=(a1)1
Step 3.2
Simplify (a-1)-1(a1)1.
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Step 3.2.1
Simplify by multiplying through.
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Step 3.2.1.1
Apply the distributive property.
a2+a=a-1-1-1a2+a=a111
Step 3.2.1.2
Simplify the expression.
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Step 3.2.1.2.1
Move -11 to the left of aa.
a2+a=-1a-1-1a2+a=1a11
Step 3.2.1.2.2
Multiply -11 by -11.
a2+a=-1a+1a2+a=1a+1
a2+a=-1a+1a2+a=1a+1
a2+a=-1a+1a2+a=1a+1
Step 3.2.2
Rewrite -1a1a as -aa.
a2+a=-a+1a2+a=a+1
a2+a=-a+1a2+a=a+1
Step 3.3
Move all terms containing aa to the left side of the equation.
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Step 3.3.1
Add aa to both sides of the equation.
a2+a+a=1a2+a+a=1
Step 3.3.2
Add aa and aa.
a2+2a=1a2+2a=1
a2+2a=1a2+2a=1
Step 3.4
Subtract 11 from both sides of the equation.
a2+2a-1=0a2+2a1=0
Step 3.5
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2ab±b24(ac)2a
Step 3.6
Substitute the values a=1a=1, b=2b=2, and c=-1c=1 into the quadratic formula and solve for aa.
-2±22-4(1-1)212±224(11)21
Step 3.7
Simplify.
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Step 3.7.1
Simplify the numerator.
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Step 3.7.1.1
Raise 22 to the power of 22.
a=-2±4-41-121a=2±441121
Step 3.7.1.2
Multiply -41-1411.
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Step 3.7.1.2.1
Multiply -44 by 11.
a=-2±4-4-121a=2±44121
Step 3.7.1.2.2
Multiply -44 by -11.
a=-2±4+421a=2±4+421
a=-2±4+421a=2±4+421
Step 3.7.1.3
Add 44 and 44.
a=-2±821a=2±821
Step 3.7.1.4
Rewrite 88 as 222222.
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Step 3.7.1.4.1
Factor 44 out of 88.
a=-2±4(2)21a=2±4(2)21
Step 3.7.1.4.2
Rewrite 44 as 2222.
a=-2±22221a=2±22221
a=-2±22221a=2±22221
Step 3.7.1.5
Pull terms out from under the radical.
a=-2±2221a=2±2221
a=-2±2221a=2±2221
Step 3.7.2
Multiply 22 by 11.
a=-2±222
Step 3.7.3
Simplify -2±222.
a=-1±2
a=-1±2
Step 3.8
The final answer is the combination of both solutions.
a=-1+2,-1-2
a=-1+2,-1-2
Step 4
The result can be shown in multiple forms.
Exact Form:
a=-1+2,-1-2
Decimal Form:
a=0.41421356,-2.41421356
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