Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you simplify and find the restrictions for $\frac{3}{x - 4} - 7$ $3/(x-4)-7$ ?

1 Answer

Aug 16, 2017

Restriction: $x \neq 4$ $color(red)(x!=4)$
Simplification (maybe): $\frac{31 - 7 x}{x - 4}$ $color(blue)((31-7x)/(x-4))$

Explanation:

Since division by $0$ $0$ is undefined.
$x - 4 \neq 0 xxx \to xxx x \neq 4$ $x-4!=0color(white)("xxx")rarrcolor(white)("xxx")x!=4$

What is considered a "simplification" is more problematic.
Here is one possibility:
$XXX \frac{3}{x - 4} - 7$ $color(white)("XXX")3/(x-4)-7$

$XXXXXX = \frac{3}{x - 4} - \frac{7 (x - 4)}{x - 4}$ $color(white)("XXXXXX")=3/(x-4)-(7(x-4))/(x-4)$

$XXXXXX = \frac{3}{x - 4} - \frac{7 x - 28}{4}$ $color(white)("XXXXXX")=3/(x-4)-(7x-28)/4$

$XXXXXX = \frac{3 - 7 x + 28}{x - 4}$ $color(white)("XXXXXX")=(3-7x+28)/(x-4)$

$XXXXXX = \frac{31 - 7 x}{x - 4}$ $color(white)("XXXXXX")=(31-7x)/(x-4)$

Related questions

See all questions in Addition and Subtraction of Rational Expressions

Impact of this question

1416 views around the world

You can reuse this answer
Creative Commons License