Solve 2x - 1 = (x + 1)÷(2x) by factorization?

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Answer 1 · 2016-01-22T04:27:48

You are going to first have to write it as a rational equation.

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

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

#4x^2# - 2x = x + 1

#4x^2# - 3x - 1 = 0

Now we can factor:

#4x^2# - 4x + x - 1 = 0

4x(x - 1) + 1(x - 1) = 0

(4x + 1)(x - 1) = 0

x = #-1/4# and 1

Don't forget to state the restrictions on the variable, which in this case would be x#!=# 0, since division by 0 is non defined.

So, x = #-1/4# and 1, x#!=# 0

Here are some practice exercises. Feel free to ask if you need help:

a) #4/x# = 2

b) #2/(x^2 + 9x + 8)#

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

b) #1/(r - 2)# + #1/(r^2 - 7r + 10)# = #6/(r - 2)#

Hopefully you understand now!