How do you multiply #1/x= (6/(5x)) + 1#?

Question

Isaiah Anthony · Accepted Answer

# 1/x#  =#6/(5x)# #+ 1# Multiplying the numerator and denominator of the L.H.S by 5: # 5/(5x)#=#6/(5x)#+ 1 # (5-6)/(5x)# #=1# # -1/(5x) = 1# #5x = -1# #x=-1/5#

Avery Alexander · Answer

undefined To solve the equation 1/x = (6/(5x)) + 1, we can start by simplifying the right side of the equation.

First, we need to find a common denominator for the fractions on the right side. The common denominator is 5x.

Next, we can rewrite the equation as follows:

1/x = (6/(5x)) + 1

To add the fractions on the right side, we need to have the same denominator.

Multiplying the numerator and denominator of 1 by 5x, we get:

1/x = (6/(5x)) + (5x/5x)

Simplifying further, we have:

1/x = (6 + 5x)/(5x)

Now, to eliminate the fraction on the left side, we can multiply both sides of the equation by x:

x * (1/x) = x * (6 + 5x)/(5x)

Simplifying, we get:

1 = (6x + 5x^2)/(5x)

To get rid of the fraction on the right side, we can multiply both sides of the equation by 5x:

5x * 1 = 5x * (6x + 5x^2)/(5x)

Simplifying further, we have:

5x = 6x + 5x^2

Rearranging the equation, we get a quadratic equation:

5x^2 + 6x - 5x = 0

Combining like terms, we have:

5x^2 + x = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.