How do you solve #\frac { 2} { z + 1} = \frac { 1} { z - 8}#?

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Answer 1 · 2017-04-03T02:29:14

Multiply both sides by the least common denominator and solve for #z#.

# z = 17#

To solve the problem it is helpful to remove the denominators.

To do this multiple both sides by the LCM of the denominators.

The LCM is # (z + 1)( z - 8 ) #

# cancel(( z + 1))( z -8) xx 2 / cancel((z +1)) = ( z+ 1)(cancel( z -8)) xx 1 /cancel(( z-8)) #

Multiplying this out removes the denominators. which results in:

# ( z -8) xx 2 = (z + 1) xx 1 " "# removing the parentheses results in

# 2z - 16 = z + 1" "# add 16 to both sides of the equation

# 2z -16 + 16 = z + 1 +16 #

# 2z = z + 17" "# Subtract #1z# from both sides to isolate #z #

# 2z- 1z = 1z - 1z + 17 # This gives

#z = 17#