Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Manipulating Rational Expressions

Manipulating Rational Expressions 1.1 - Solution

arrow_back Return to Manipulating Rational Expressions
a
We can simplify the expression if we can factor out the same factors in the numerator and the denominator, and then let them cancel each other out. All terms in the numerator and also the denominator is divisible by 44 so we can factor this factor out.
16+8x4x4x2\dfrac{16+8x}{4x-4x^2}
44+42x4x4x2\dfrac{4\cdot 4+4\cdot 2x}{4\cdot x-4\cdot x^2}
4(4+2x)4(xx2)\dfrac{4\left(4+2x\right)}{4\left(x-x^2\right)}
4+2xxx2\dfrac{4+2x}{x-x^2}
Even if we can still factor out a 22 in the numerator and xx in the denominator, these factors can not cancel each other out.
b
All terms contain x.x. This means that we can factor out the xx in both the numerator and the denominator and have them cancel each other out.
x22xx3+3x\dfrac{x^2-2x}{x^3+3x}
xxx2xx2+x3\dfrac{x\cdot x-x\cdot 2}{x\cdot x^2+x\cdot 3}
x(x2)x(x2+3)\dfrac{x\left(x-2\right)}{x\left(x^2+3\right)}
x2x2+3\dfrac{x-2}{x^2+3}
c
It is not clear which factors of the numerator and denominator have in common. Let's start by factoring out 3.3.
3x9x23x\dfrac{3x-9}{x^2-3x}
3x33xxx3\dfrac{3\cdot x-3\cdot 3}{x\cdot x-x\cdot 3}
3(x3)x(x3)\dfrac{3(x-3)}{x(x-3)}
Now we see that the numerator and the denominator share a factor x3.x-3.
3(x3)x(x3)\dfrac{3(x-3)}{x(x-3)}
3x\dfrac{3}{x}