1. (2x-6)/(21) divided by (5x-15)/(12)
2. Solve (x)/(x-9)-4=(9)/(x-9)..I got -6, is that correct?
3. Add. Express your answer in simplest form...(4)/(s)+(6)/(s^2)..
4. Add. Express your answer in simplest form...(x^2)/(x+4)+(8x+16)/(x+4)
Lets check you number 2)
-6/(-15) - 4= 9/(-15)
6/15-4= ?
-3 7/15 does not equal -9/15
Show your work. You wont find many here that will do these for you.
On question #1, you multiply the first number by the inverse of the other.
So what's:
(2x-6)/21 * 12/(5x-15)
Question 2 seems impossible to me. But I might be doing it wrong...it's almost midnight here.
I subtracted the (x)/(x-9) on both sides and came up with the equation:
-4 = (9-x)/(x-9) No matter what you plug into there, it will be -1. And
-4 does not equal -1.
Wait for someone else's confirmation on that though.
On question #3, here's a hint. If you multiply something by 1, it will still stay the same. s/s = 1. See what you can do with that.
#4 - add the numerators straight across. You MAY be able to factor it out and get rid of the denominator. You'll have to try it out to see.
As you post your work, we can critique it.
1. To divide fractions, you can simplify the expression by multiplying the first fraction by the reciprocal of the second fraction.
So, to divide (2x-6)/21 by (5x-15)/12, we multiply the first fraction by the reciprocal of the second fraction:
(2x-6)/21 * 12/(5x-15)
Now, we can simplify this expression.
First, we can simplify the numerator:
(2x-6) * 12 = 24x - 72
Next, we can simplify the denominator:
21 * (5x-15) = 105x - 315
So, the simplified expression becomes:
(24x - 72)/(105x - 315)
2. To solve the equation (x)/(x-9) - 4 = (9)/(x-9), let's first multiply both sides of the equation by (x-9) to eliminate the denominators:
(x)/(x-9) * (x-9) - 4 * (x-9) = (9)/(x-9) * (x-9)
This simplifies to:
x - 4(x-9) = 9
Next, we can distribute -4 to (x-9):
x - 4x + 36 = 9
Combine the like terms:
-3x + 36 = 9
Subtract 36 from both sides:
-3x = 9 - 36
-3x = -27
Finally, divide both sides by -3 to solve for x:
x = -27 / -3
x = 9
So, the solution to the equation is x = 9.
3. To add the fractions (4)/(s) + (6)/(s^2), we need to have a common denominator.
The common denominator for these fractions is s^2.
To get the denominators to be the same, we multiply the first fraction by (s^2)/(s^2) and the second fraction by (s)/(s):
(4)/(s) * (s^2)/(s^2) + (6)/(s^2) * (s)/(s)
This simplifies to:
(4s^2)/(s^2) + (6s)/(s^2)
Now, we can add the numerators:
(4s^2 + 6s)/(s^2)
Since there are no like terms in the numerator, we cannot simplify this expression any further.
Therefore, the sum of (4)/(s) + (6)/(s^2) is (4s^2 + 6s)/(s^2).
4. To add the fractions (x^2)/(x+4) + (8x+16)/(x+4), we simply add the numerators straight across, while keeping the common denominator:
(x^2 + 8x + 16)/(x+4)
The numerator cannot be factored further, so the sum in simplest form is (x^2 + 8x + 16)/(x+4).
1. To divide one fraction by another, you can multiply the first fraction by the reciprocal of the second fraction. So, the division problem becomes:
(2x-6)/(21) ÷ (5x-15)/(12)
This is equivalent to:
(2x-6)/(21) * (12)/(5x-15)
Next, simplify by canceling out common factors:
[(2x-6) * (12)] / [(21) * (5x-15)]
= (24x - 72) / (105x - 315)
Therefore, (2x-6)/(21) ÷ (5x-15)/(12) simplifies to (24x - 72) / (105x - 315).
2. To solve the equation (x)/(x-9) - 4 = (9)/(x-9), we need to isolate the variable x.
First, we can simplify the equation:
(x)/(x-9) - 4 = (9)/(x-9)
Multiply both sides of the equation by (x-9) to eliminate the denominators:
(x) - 4(x-9) = (9)
Distribute -4 on the left side:
x - 4x + 36 = 9
Combine like terms:
-3x + 36 = 9
Subtract 36 from both sides:
-3x = -27
Divide both sides by -3:
x = 9
Therefore, the solution for the equation (x)/(x-9) - 4 = (9)/(x-9) is x = 9.
3. To add (4)/(s) + (6)/(s^2), we need to have a common denominator.
The least common denominator (LCD) for (s) and (s^2) is s^2.
Multiply the first fraction by (s)/(s) and the second fraction by (s)/(s):
[(4)/(s)] * (s)/(s) + [(6)/(s^2)] * (s)/(s)
This gives us:
(4s)/(s^2) + (6s)/(s^3)
Combining the fractions gives us:
(4s + 6s)/(s^2)
Simplifying the numerator:
(10s)/(s^2)
Therefore, (4)/(s) + (6)/(s^2) simplifies to (10s)/(s^2).
4. To add (x^2)/(x+4) + (8x+16)/(x+4), we combine the numerators over the common denominator:
[(x^2) + (8x + 16)] / (x + 4)
Simplifying the numerator:
(x^2 + 8x + 16) / (x + 4)
We can notice that the numerator can be factored:
(x + 4)(x + 4) / (x + 4)
Canceling out the common factor in the numerator and denominator:
(x + 4)
Therefore, (x^2)/(x+4) + (8x+16)/(x+4) simplifies to (x + 4).