How do you multiply #3 /(x - 1) + 1 / (x(x - 1)) = 2 / x#?

Question

How do you multiply #3 /(x - 1)    +   1 / (x(x - 1)) =  2 / x#?

Isaiah Anthony · Accepted Answer

Assuming the question really was "solve for "#x#:
#color(white)("XXX")x=-3# 1 Multiply both sides by the Least Common Denominator [namely #x(x-1)#] #color(white)("XXX")3x+1=2(x-1)# 2 Simplify #color(white)("XXX")3x+1=2x-2# 3 Subtract #2x# from both sides #color(white)("XXX")3x+1-2x=-2# 4 Simplify #3x+1-2x# to #x+1# #color(white)("XXX")x+1=-2# 5 Subtract #1# from both sides #color(white)("XXX")x=-2-1# 6 Simplify #color(white)("XXX")x=-3#

Kennedy Adams · Answer

#x=-3#

Multiply the first fraction by #x#

#[3x+1]/[x(x-1)]=2/x#

Now multiply both sides by #x(x-1)# to remove the fractions

#3x+1=2(x-1)#

#3x+1=2x-2#

subtract #2x# from both sides

#x+1=-2#

subtract 1 from both sides

Hazel Anglin · Answer

undefined To solve the equation 3/(x - 1) + 1/(x(x - 1)) = 2/x, we need to find a common denominator and combine the fractions. The common denominator for the fractions is x(x - 1). Multiplying each term by x(x - 1), we get:

3(x(x - 1))/(x - 1) + 1/(x(x - 1)) = 2(x(x - 1))/x

Simplifying further:

3x + 3 - 1 = 2(x - 1)

Expanding and simplifying:

3x + 3 - 1 = 2x - 2

Combining like terms:

3x + 2 = 2x - 2

Subtracting 2x from both sides:

x + 2 = -2

Subtracting 2 from both sides:

x = -4

Therefore, the solution to the equation is x = -4.