Question

Simplify 4 x all over 9 plus quantity x minus 10 over 9

Answer 1

4x/9 + (x-10)/9
Since both fractions have a common denominator, you can just add across:
= (4x+x-10)/9
= (5x-10)/9
= 5(x-2)/9

Answer 2

I see! how do you solve a rational expression when the denominator is diffrent? like Simplify 3 over x plus 13 over quantity x minus 11 ?

Answer 3

Since we are working with an expression and not an equation it can't be simplified in this case, unless the denominators were multiples of each other.

If it was an equation then you would do this:
Starting with \[3/x+13/(x-11)=0\]
Move 3/x to the other side
\[13/(x-11)=-3/x\]
Multiply both sides by x
\[13x/(x-11)=-3\]
Multiply both sides by x-11
\[13x=-3(x-11)\]
Simplify and put all terms on one side
\[16x-33=0\]

Answer 4

Is it the same if their both expressions? or do you have to solve them diffrently?

Answer 5

With an expression you don't have an "equal sign" so you can't move things to the other side. Expressions don't have explicit solutions either, they are just a mathermatical relationship.

An equation however has a set of particular solutions that make the equation valid, hence the equal sign.

So the expression
\[3/x+13/(x-11)\]
is already simplified because the "x-11" has an addition term that the other denominator does not.

The equation
\[3/x+13/(x-11)=0\]
however has an equal sign that lets you do more with it

Answer 6

I'm such a dunce! Of course it's an equation if there's an Equal sign. The title of my assignment threw me of... Thank you so much for your help!

Answer 7

Hehe, no problem!