How do you solve #2/(x +6) = 9/8 - 4/(x+6)#?

Question

Avery Alexander · Accepted Answer

#x=-2/3#

Original solution Place on a common denominator and solve the resulting linear equation. #16/(8x + 48)# = #(9x + 54)/ (8x + 48)# - #32/(8x + 48)#

16 - 54 + 32 = 9x

-6 = 9x

#-2/3# = x

Simplier solution #2/(x+6)=9/8-4/(x+6)# #2/(x+6)+4/(x+6)=9/8# #6/(x+6)=9/8# Multiply both sides by #(x+6)# and divide by #9/8# #6*8/9=x+6# #x=(2*8)/3-6=16/3-6=5 1/3-6=-2/3# The solution is #-2/3#.

Abigail Allen · Answer

undefined To solve the equation 2/(x + 6) = 9/8 - 4/(x + 6), we can start by simplifying the right side of the equation.

First, find a common denominator for the fractions on the right side, which is 8(x + 6).

Rewriting the equation with the common denominator, we have:

2/(x + 6) = (9/8)(8(x + 6)) - (4/(x + 6))(8(x + 6))

Simplifying further, we get:

2/(x + 6) = 9(x + 6) - 4(8)

Expanding and simplifying the right side, we have:

2/(x + 6) = 9x + 54 - 32

Combining like terms, we get:

2/(x + 6) = 9x + 22

Next, we can eliminate the fraction by multiplying both sides of the equation by (x + 6).

This gives us:

2 = (9x + 22)(x + 6)

Expanding the right side, we have:

2 = 9x^2 + 96x + 132

Rearranging the equation to have zero on one side, we get:

9x^2 + 96x + 132 - 2 = 0

Simplifying further, we have:

9x^2 + 96x + 130 = 0

At this point, we can either factor the quadratic equation or use the quadratic formula to find the values of x.

Factoring the equation, we have:

(3x + 10)(3x + 13) = 0

Setting each factor equal to zero, we get:

3x + 10 = 0 or 3x + 13 = 0

Solving for x in each equation, we have:

3x = -10 or 3x = -13

x = -10/3 or x = -13/3

Therefore, the solutions to the equation 2/(x + 6) = 9/8 - 4/(x + 6) are x = -10/3 and x = -13/3.