Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you simplify $\frac{4 x - 9}{2 x - 3}$ $(4x-9)/(2x-3)$ ?

2 Answers

Jun 17, 2018

$\frac{4 x - 9}{2 x - 3} = 2 - \frac{3}{2 x - 3} xxxxx$ $(4x-9)/(2x-3)=color(blue)(2-3/(2x-3))color(white)"xxxxx"$ ...but it is not clear that this is a "simplification"

Explanation:

Since this was asked under "Excluded Values for Rational Expression" perhaps it should be noted that
$XXX \frac{4 x - 9}{2 x - 3}$ $color(white)("XXX")(4x-9)/(2x-3)$ is not defined if $(2 x - 3) = 0 \to x = \frac{3}{2}$ $(2x-3)=0 rarr x=3/2$

Jun 17, 2018

$2 - \frac{3}{2 x - 3}$ $2-3/(2x-3)$

Explanation:

Given: $\frac{4 x - 9}{2 x - 3}$ $(4x-9)/(2x-3)$

Starting the same process as long division (this one is short)

$ddddd.ddddd 4 x - 9$ $color(white)("ddddd.ddddd")4x-9$
$color(magenta)(2)(2x-3)-> ul(4x-6larr" Subtract")$
$color(white)("dddddddddddd")0color(magenta)(-3 larr" Remainder")$

$(4x-9)-:(2x-3) = color(magenta)(2-3/(2x-3))$

Related questions

See all questions in Excluded Values for Rational Expressions

Impact of this question

4170 views around the world

You can reuse this answer
Creative Commons License