How To
Given a complex rational expression, simplify it.
Combine the expressions in the numerator into a single rational expression by adding or subtracting.
Combine the expressions in the denominator into a single rational expression by adding or subtracting.
Rewrite as the numerator divided by the denominator.
Rewrite as multiplication.
Multiply.
Simplify.
Simplifying complex rational expressions
Simplify:
$\frac{y+\frac{1}{x}}{\frac{x}{y}}$ .
Begin by combining the expressions in the numerator into one expression.
$$\begin{array}{cc}y\cdot \frac{x}{x}+\frac{1}{x}\hfill & \phantom{\rule{2em}{0ex}}\text{\hspace{1em}\hspace{1em}}\text{Multiplyby}\frac{x}{x}\text{togetLCDasdenominator}.\hfill \\ \frac{xy}{x}+\frac{1}{x}\hfill & \\ \frac{xy+1}{x}\hfill & \phantom{\rule{2em}{0ex}}\text{\hspace{1em}\hspace{1em}}\text{Addnumerators}.\hfill \end{array}$$
Now the numerator is a single rational expression and the denominator is a single rational expression.
$\frac{\frac{xy+1}{x}}{\frac{x}{y}}$
We can rewrite this as division, and then multiplication.
$$\begin{array}{cc}\frac{xy+1}{x}\xf7\frac{x}{y}\hfill & \\ \frac{xy+1}{x}\cdot \frac{y}{x}\hfill & \phantom{\rule{2em}{0ex}}\text{Rewriteasmultiplication}\text{.}\hfill \\ \frac{y(xy+1)}{{x}^{2}}\hfill & \phantom{\rule{2em}{0ex}}\text{Multiply}\text{.}\hfill \end{array}$$
Got questions? Get instant answers now! Got questions? Get instant answers now!
Q&A
Can a complex rational expression always be simplified?
Yes. We can always rewrite a complex rational expression as a simplified rational expression.
Key concepts
Rational expressions can be simplified by cancelling common factors in the numerator and denominator. See
[link] .
We can multiply rational expressions by multiplying the numerators and multiplying the denominators. See
[link] .
To divide rational expressions, multiply by the reciprocal of the second expression. See
[link] .
Adding or subtracting rational expressions requires finding a common denominator. See
[link] and
[link] .
Complex rational expressions have fractions in the numerator or the denominator. These expressions can be simplified. See
[link] .
Section exercises
Verbal
How can you use factoring to simplify rational expressions?
You can factor the numerator and denominator to see if any of the terms can cancel one another out.
Got questions? Get instant answers now!
Tell whether the following statement is true or false and explain why: You only need to find the LCD when adding or subtracting rational expressions.
True. Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms.
Got questions? Get instant answers now!
Algebraic
For the following exercises, simplify the rational expressions.
For the following exercises, multiply the rational expressions and express the product in simplest form.
Questions & Answers
x-2y+3z=-3
2x-y+z=7
-x+3y-z=6
Need help solving this problem (2/7)^-2
what is the coefficient of -4×
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
If f(x) = x-2
then, f(3) when 5f(x+1)
5((3-2)+1)
5(1+1)
5(2)
10
Augustine
how do they get the third part x = (32)5/4
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
can someone help me with some logarithmic and exponential equations.
sure. what is your question?
ninjadapaul
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2
so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
is it a question of log
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.