How do you simplify #(7x-1)/(2x+3)#?

1 Answer
Andy Y.
Jun 5, 2017

Using long division: #1/2(7 + 23/(2x+3))#

Explanation:

In one sense, this rational expression is in lowest possible terms already. Neither the numerator nor the denominator can factor. All the numbers (or coefficients) are prime numbers.

However, you could do long division to express this with a single instance of the variable #x# instead of two instances.

#color(white)(aaaaaaa)7/2 + 23/(2(2x+3))#
#2x+3 |bar(7x-1color(white)(aaaaaaa))#
#color(white)(aaa|)-ul((7x-21/2)#
#color(white)(aaaaaaaaaaaa)23/2#

Then, factor out the common #1/2# to get

#1/2(7 + 23/(2x+3))#

However, it is arguable whether this is actually "simpler" than the original.

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