Add 1/(1+x)+(1-x)/x

Math
11+x+1-xx
To write 11+x as a fraction with a common denominator, multiply by xx.
11+x⋅xx+1-xx
To write 1-xx as a fraction with a common denominator, multiply by 1+x1+x.
11+x⋅xx+1-xx⋅1+x1+x
Write each expression with a common denominator of (1+x)x, by multiplying each by an appropriate factor of 1.
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Multiply 11+x and xx.
x(1+x)x+1-xx⋅1+x1+x
Multiply 1-xx and 1+x1+x.
x(1+x)x+(1-x)(1+x)x(1+x)
Reorder the factors of (1+x)x.
xx(1+x)+(1-x)(1+x)x(1+x)
xx(1+x)+(1-x)(1+x)x(1+x)
Combine the numerators over the common denominator.
x+(1-x)(1+x)x(1+x)
Simplify the numerator.
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Expand (1-x)(1+x) using the FOIL Method.
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Apply the distributive property.
x+1(1+x)-x(1+x)x(1+x)
Apply the distributive property.
x+1⋅1+1x-x(1+x)x(1+x)
Apply the distributive property.
x+1⋅1+1x-x⋅1-x⋅xx(1+x)
x+1⋅1+1x-x⋅1-x⋅xx(1+x)
Simplify and combine like terms.
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Simplify each term.
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Multiply 1 by 1.
x+1+1x-x⋅1-x⋅xx(1+x)
Multiply x by 1.
x+1+x-x⋅1-x⋅xx(1+x)
Multiply -1 by 1.
x+1+x-x-x⋅xx(1+x)
Multiply x by x by adding the exponents.
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Move x.
x+1+x-x-(x⋅x)x(1+x)
Multiply x by x.
x+1+x-x-x2x(1+x)
x+1+x-x-x2x(1+x)
x+1+x-x-x2x(1+x)
Subtract x from x.
x+1+0-x2x(1+x)
Add 1 and 0.
x+1-x2x(1+x)
x+1-x2x(1+x)
Reorder terms.
-x2+x+1x(1+x)
-x2+x+1x(1+x)
Simplify with factoring out.
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Factor -1 out of -x2.
-(x2)+x+1x(1+x)
Factor -1 out of x.
-(x2)-1(-x)+1x(1+x)
Factor -1 out of -(x2)-1(-x).
-(x2-x)+1x(1+x)
Rewrite 1 as -1(-1).
-(x2-x)-1(-1)x(1+x)
Factor -1 out of -(x2-x)-1(-1).
-(x2-x-1)x(1+x)
Simplify the expression.
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Rewrite -(x2-x-1) as -1(x2-x-1).
-1(x2-x-1)x(1+x)
Move the negative in front of the fraction.
-x2-x-1x(1+x)
-x2-x-1x(1+x)
-x2-x-1x(1+x)
Add 1/(1+x)+(1-x)/x

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