Simplify this algebraic expression

In summary, when simplifying the expression x(9x+2) / x3(x-2), it is possible to cancel the "x" factor in the numerator and "x^3" in the denominator, leaving the simplest form of (9x+2)^2/(x-2). However, it is incorrect to cancel terms that are not factors, and using parentheses is necessary when there are two or more terms in the numerator or denominator.
  • #1
Gringo123
141
0
How can I simplify this expression? As it is already factorised (factored) I do not see what else I can do to simplify it.

x(9x+2) / x3(x-2)

The only thing that I can think of is if I unfactorise everything to give the following:(although it doesn't seem to be very simplified from the original expression)

x2 + 2x / x4 - 2x3

which gives... 2x / x2 - 2x3
 
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  • #2
General rule- never "unfactorize" unless you see very good reason to!

Here, you should be able to see the "x" factor in the numerator and "[itex]x^3[/itex]" in the denominator and immediately cancel. What's left, 9x+2 and x- 2, have no common factor so the simplest form is [itex](9x+2)^2/(x-2)[/itex]

In what you wrote, you seem to have forgotten the "9" in the numerator.

Also, you cannot cancel, in numerator and denominator, things that are added. [itex](x^2+ 2x)/(x^4- 2x^3)[/itex] is NOT [itex]2x/(x^2- 2x^3)[/itex].
 
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  • #3
Thanks a lot Hall of Ivy!
 
  • #4
Gringo123 said:
How can I simplify this expression? As it is already factorised (factored) I do not see what else I can do to simplify it.

x(9x+2) / x3(x-2)

The only thing that I can think of is if I unfactorise everything to give the following:(although it doesn't seem to be very simplified from the original expression)

x2 + 2x / x4 - 2x3

which gives... 2x / x2 - 2x3

Whenever there are two or more terms in the numerator or denominator, parentheses are needed around the numerator or denominator, or both.

More seriously, you are cancelling terms in the numerator or denominator that are not factors. By this same logic we would say that (1 + 2)/(2 + 7) = 1/7, which is clearly incorrect.
 

1. How do I simplify this algebraic expression?

To simplify an algebraic expression, you need to combine like terms and perform any necessary operations such as addition, subtraction, multiplication, and division. You can also use the distributive property to simplify expressions with parentheses.

2. What are the steps to simplify an algebraic expression?

The steps to simplify an algebraic expression are:1. Combine like terms2. Use the distributive property if necessary3. Perform any operations (addition, subtraction, multiplication, or division) to simplify the expression further.

3. Can I use the order of operations to simplify an algebraic expression?

Yes, the order of operations (PEMDAS) can be applied when simplifying an algebraic expression. It helps to determine which operations should be performed first.

4. Are there any rules I need to follow when simplifying an algebraic expression?

There are several rules that can help simplify algebraic expressions, such as the commutative, associative, and distributive properties. It is also important to remember to combine like terms and follow the order of operations.

5. Is there a specific way to check if I have simplified an algebraic expression correctly?

Yes, you can check if you have simplified an algebraic expression correctly by substituting values for the variables and comparing the original expression with the simplified one. The two expressions should give the same result for any given values of the variables.

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