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

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)

Expand (1-x)(1+x) using the FOIL Method.

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.

Simplify each term.

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.

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)

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.

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