please help. Algebra 2 rational equation

Question

3/4+ 1/x-1= 6/x-1 solve and show work

algebra 2 rational equations

lesson twenty five

find Least common denominator

Answer 1

(3/4) + 1/(x-1) = 6/(x-1) original equation

(3/4) = 6/(x-1) - 1/(x-1) rearrange to group similar denominators

(3/4) = 5/(x-1) subtract

3*(x-1) = 4*5 cross multiply both sides of the equation

3x - 3 = 20 distribute the 3 inside the parentheses

3x = 20 + 3 rearrange to isolate the variable (x)

3x = 23 add

x = 23/3 divide

Answer 2

The common denominator for this is 4(x-1)

Multiply both sides of the equation by the common denominator to get:

3/4(4)(x-1)+ 1/(x-1)(4)(x-1)= 6/(x-1)(4)(x-1) Simplify

3(x-1) +1(4) = 6(4) Simplify

3x-3+4=24 Combine like terms

3x+1=24 Subtract 1 from both sides

3x+1-1=24-1 Simplify

3x=23 Divide by 3

x=23/3