1x-1+5=11x-1

Subtract 5 from both sides of the equation.

1x-1=11x-1-5

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

x-1,x-1,1

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The number 1 is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of 1,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.

1

The factor for x-1 is x-1 itself.

(x-1)=x-1

(x-1) occurs 1 time.

The LCM of x-1,x-1 is the result of multiplying all factors the greatest number of times they occur in either term.

x-1

x-1

Multiply each term in 1x-1=11x-1-5 by x-1 in order to remove all the denominators from the equation.

1x-1⋅(x-1)=11x-1⋅(x-1)-5⋅(x-1)

Cancel the common factor of x-1.

Cancel the common factor.

1x-1⋅(x-1)=11x-1⋅(x-1)-5⋅(x-1)

Rewrite the expression.

1=11x-1⋅(x-1)-5⋅(x-1)

1=11x-1⋅(x-1)-5⋅(x-1)

Simplify 11x-1⋅(x-1)-5⋅(x-1).

Simplify each term.

Cancel the common factor of x-1.

Cancel the common factor.

1=11x-1⋅(x-1)-5⋅(x-1)

Rewrite the expression.

1=11-5⋅(x-1)

1=11-5⋅(x-1)

Apply the distributive property.

1=11-5x-5⋅-1

Multiply -5 by -1.

1=11-5x+5

1=11-5x+5

Add 11 and 5.

1=-5x+16

1=-5x+16

1=-5x+16

Rewrite the equation as -5x+16=1.

-5x+16=1

Move all terms not containing x to the right side of the equation.

Subtract 16 from both sides of the equation.

-5x=1-16

Subtract 16 from 1.

-5x=-15

-5x=-15

Divide each term by -5 and simplify.

Divide each term in -5x=-15 by -5.

-5x-5=-15-5

Cancel the common factor of -5.

Cancel the common factor.

-5x-5=-15-5

Divide x by 1.

x=-15-5

x=-15-5

Divide -15 by -5.

x=3

x=3

x=3

Solve for x 1/(x-1)+5=11/(x-1)