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Basic Math Examples
aa-1=-1a+1aa−1=−1a+1
Step 1
Move the negative in front of the fraction.
aa-1=-1a+1aa−1=−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)=(a−1)⋅−1
Step 3
Step 3.1
Simplify a(a+1)a(a+1).
Step 3.1.1
Rewrite.
0+0+a(a+1)=(a-1)⋅-10+0+a(a+1)=(a−1)⋅−1
Step 3.1.2
Simplify by adding zeros.
a(a+1)=(a-1)⋅-1a(a+1)=(a−1)⋅−1
Step 3.1.3
Apply the distributive property.
a⋅a+a⋅1=(a-1)⋅-1a⋅a+a⋅1=(a−1)⋅−1
Step 3.1.4
Simplify the expression.
Step 3.1.4.1
Multiply aa by aa.
a2+a⋅1=(a-1)⋅-1a2+a⋅1=(a−1)⋅−1
Step 3.1.4.2
Multiply aa by 11.
a2+a=(a-1)⋅-1a2+a=(a−1)⋅−1
a2+a=(a-1)⋅-1a2+a=(a−1)⋅−1
a2+a=(a-1)⋅-1a2+a=(a−1)⋅−1
Step 3.2
Simplify (a-1)⋅-1(a−1)⋅−1.
Step 3.2.1
Simplify by multiplying through.
Step 3.2.1.1
Apply the distributive property.
a2+a=a⋅-1-1⋅-1a2+a=a⋅−1−1⋅−1
Step 3.2.1.2
Simplify the expression.
Step 3.2.1.2.1
Move -1−1 to the left of aa.
a2+a=-1⋅a-1⋅-1a2+a=−1⋅a−1⋅−1
Step 3.2.1.2.2
Multiply -1−1 by -1−1.
a2+a=-1⋅a+1a2+a=−1⋅a+1
a2+a=-1⋅a+1a2+a=−1⋅a+1
a2+a=-1⋅a+1a2+a=−1⋅a+1
Step 3.2.2
Rewrite -1a−1a as -a−a.
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.
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+2a−1=0
Step 3.5
Use the quadratic formula to find the solutions.
-b±√b2-4(ac)2a−b±√b2−4(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)2⋅1−2±√22−4⋅(1⋅−1)2⋅1
Step 3.7
Simplify.
Step 3.7.1
Simplify the numerator.
Step 3.7.1.1
Raise 22 to the power of 22.
a=-2±√4-4⋅1⋅-12⋅1a=−2±√4−4⋅1⋅−12⋅1
Step 3.7.1.2
Multiply -4⋅1⋅-1−4⋅1⋅−1.
Step 3.7.1.2.1
Multiply -4−4 by 11.
a=-2±√4-4⋅-12⋅1a=−2±√4−4⋅−12⋅1
Step 3.7.1.2.2
Multiply -4−4 by -1−1.
a=-2±√4+42⋅1a=−2±√4+42⋅1
a=-2±√4+42⋅1a=−2±√4+42⋅1
Step 3.7.1.3
Add 44 and 44.
a=-2±√82⋅1a=−2±√82⋅1
Step 3.7.1.4
Rewrite 88 as 22⋅222⋅2.
Step 3.7.1.4.1
Factor 44 out of 88.
a=-2±√4(2)2⋅1a=−2±√4(2)2⋅1
Step 3.7.1.4.2
Rewrite 44 as 2222.
a=-2±√22⋅22⋅1a=−2±√22⋅22⋅1
a=-2±√22⋅22⋅1a=−2±√22⋅22⋅1
Step 3.7.1.5
Pull terms out from under the radical.
a=-2±2√22⋅1a=−2±2√22⋅1
a=-2±2√22⋅1a=−2±2√22⋅1
Step 3.7.2
Multiply 22 by 11.
a=-2±2√22
Step 3.7.3
Simplify -2±2√22.
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…