Solve Rational Expressions: x/20 = (3/8)-(4/5)

In summary, when solving the equation \frac{3}{8}- \frac{4}{5}, we first find the common denominator, which is 40. Then we can write the equation as \frac{15}{40} - \frac{32}{40}, which simplifies to \frac{15-32}{40} = \frac{-17}{40}. This means that the value of x is -8.5. However, it is important to note that the process of finding the LCM and factoring may not always result in the correct answer, as seen in this conversation where the final answer was questioned.
  • #1
ramstin
18
0
1. x/20 = (3/8)-(4/5)



2. solve



3. My attempt as far as I can tell there is no LCM so

3/8 becomes 15/40 4/5 becomes 32/40

(15/40)-(32/40)= 17/40 which equals 8.5/20 which means x=8.5




For some reason I don't think I got the right answer?
 
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  • #2
ramstin said:
(15/40)-(32/40)= 17/40 which equals 8.5/20 which means x=8.5

For some reason I don't think I got the right answer?


[tex]\frac{15}{40}- \frac{32}{40} \neq \frac{17}{40}[/tex]


15/40 is less than 32/40. Do you think you answer would be positive?

If you have to find 3-4, you won't get 1. You'd get -1.
 
  • #3
o.k. how do you get a LCM to factor with if the only LCM is 1?

Man I am confused :P
 
  • #4
ramstin said:
o.k. how do you get a LCM to factor with if the only LCM is 1?

Man I am confused :P

Let's start over then.

[tex]\frac{3}{8}- \frac{4}{5}[/tex]


We agree that the common denominator is 40,right?


[tex]\frac{3}{8}- \frac{4}{5}= \frac{15}{40} - \frac{32}{40}[/tex]

Understand up to here right?


Now, if the denominators are the same, you can write it as one single fraction like so:

[tex]\frac{15}{40} - \frac{32}{40}= \frac{15-32}{40}[/tex]


Now you must find the value of 15-32
 
  • #5
so that would be -17


-17/40 so it would be -8.5
 
  • #6
I guess what is confusing me is that the assignment was about solving equations after finding and factoring the LCM.
 
  • #7
ramstin said:
so that would be -17


-17/40 so it would be -8.5

Yep..
 

1. What are rational expressions?

Rational expressions are algebraic expressions that involve fractions with variables in the numerator and/or denominator. They are used to represent relationships between quantities and can be simplified using algebraic operations.

2. How do I solve rational expressions?

To solve rational expressions, you need to find the common denominator and combine the fractions into one expression. Then, use algebraic operations to simplify the expression and solve for the variable.

3. What is the common denominator?

The common denominator is the lowest common multiple of the denominators in the rational expression. It is used to combine fractions and make it easier to simplify the expression.

4. What do I do if there is a variable in the denominator?

If there is a variable in the denominator, you can multiply both the numerator and denominator by that variable to eliminate it. This will not change the value of the expression.

5. How do I check my answer for rational expressions?

You can check your answer by substituting the value you found for the variable back into the original expression and simplifying it. If the simplified expression equals the original expression, then your answer is correct.

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