can anyone explain how to divide in algebra? I have this problem:
(15x2-24+9)/(3x-3)
I am not looking for someone to give me the answer straight out I just need to know how to get there.
Start in the same way as you would do long division.
Set it up as
_________
(3x-3)|15x2-24x+9
then how many times does 3x go into 15x^2, which is 5x
5x
_________
(3x-3)|15x2-24x+9
15x2-15x (from 5x times (3x-3)
subtract
5x
_________
(3x-3)|15x2-24x+9
15x2-15x
________
-9x+9
I hope the formatting holds. Is this OK?
The formatting didn't work 8-((
I hope you get the idea. I'll try again with dots for spaces.
Start in the same way as you would do long division.
Set it up as
......_________
(3x-3)|15x2-24x+9
then how many times does 3x go into 15x^2, which is 5x
.......5x
......._________
(3x-3)|15x2-24x+9
.......15x2-15x (from 5x times (3x-3)
subtract
.......5x
......._________
(3x-3)|15x2-24x+9
.......15x2-15x
............________
............-9x+9
Sure! I'd be happy to explain how to perform division in algebra.
To divide algebraic expressions, follow these steps:
Step 1: Factor as much as possible.
In your problem: (15x^2 - 24 + 9) / (3x - 3), there are no common factors that can be factored out further. So, we move to the next step.
Step 2: Rewrite the division as multiplication using the reciprocal of the denominator.
Since division can be written as multiplication by the reciprocal, rewrite the expression as: (15x^2 - 24 + 9) * (1/(3x - 3)).
Step 3: Perform the multiplication using the distributive property.
Distribute each term in the numerator by multiplying it by the reciprocal of the denominator:
(15x^2 - 24 + 9) * (1/(3x - 3))
= (15x^2 * 1/(3x - 3)) + (-24 * 1/(3x - 3)) + (9 * 1/(3x - 3))
Step 4: Simplify the expression.
Now, we simplify each term separately:
Term 1: (15x^2 * 1/(3x - 3))
When multiplying variables with exponents, add the exponents:
= (15x^2/(3x - 3))
Term 2: (-24 * 1/(3x - 3))
= (-24/(3x - 3))
Term 3: (9 * 1/(3x - 3))
= (9/(3x - 3))
Step 5: Combine the simplified terms.
Combine the simplified terms into a single expression:
(15x^2/(3x - 3)) + (-24/(3x - 3)) + (9/(3x - 3))
Step 6: Factor out any common factors if possible.
In this case, you can factor out 3 from each term in the denominator:
= (15x^2 - 8 + 3)/(3(x - 1))
So, the final simplified expression is:
(15x^2 - 8 + 3)/(3(x - 1))
Now, you can simplify it further, if possible.