Answer:
1. Option C is correct
2. Option A is correct
3. Option C is correct
4. Option B is correct
5. Option D is correct
Step-by-step explanation:
1. x^2-3x-18/x+3
Factorize the numerator
x^2-6x+3x-18/x+3
x(x-6)+3(x-6)/x+3
(x+3)(x-6)/x+3
x-6
x-6 where x≠6
Option C is correct.
2. x-2/x^2+4x-12
Factorizing the denominator
x-2/x^2+6x-2x-12
x-2/x(x+6)-2(x+6)
x-2/(x-2)(x+6)
1/x+6
1/x+6 where x≠-6
Option A is correct.
3. 5x^3/7 x^3+x^4
5x^3/7x^3+x^4
5x^3/x^3(7+x)
5/7+x
Option C is correct
5/7+x where x≠-7
4. Simplify x/6x-x^2
x/6x-x^2
x/x(6-x)
1/6-x
Option B is correct
1/6-x where x≠6
5. 2/3a * 2/a^2
Multiplying both terms
4/3a^3
Option D is correct.
4/3a^3 where a≠0
Answer:
b = -8
Step-by-step explanation:
crossmultiply
Answer:
The other rational number in the operation given is:
Step-by-step explanation:
To obtain the number in the operation given, we're gonna represent the operation:
Where:
- r = the other rational number.
Now we are going to solve r to identify its value in numbers:
- (We pass a number that is multiplying to the left of the equal, to divide to the right of the equal symbol)
As you can see, when we operate, <u>the result is 6/5</u>, and we can prove this multiplying as we had in the original equation, replacing r by 6/5:
- r * 15/14 = 9/7
- 6/5 * 15/14 = 9/7
- 9/7 = 9/7
In this form, we know the result is correct.
Answer:
Equivalent
Step-by-step explanation:
Look at 6/18. 18 divided by 6 is 3, which is the denominator. 6 divided by 6 is 1, so the numerator. So 1/3.
Answer:
Time required by Ben was 12 minutes.
Step-by-step explanation:
Given:
Time Required for Fred = 16 mins
Ben completed his run in 3/4 of the amount of time of Freds run.
We need to find the time required by Ben.
Now Given that;
Ben completed his run in 3/4 of the amount of time of Freds run.
It means that time required by Ben is equal to 3/4 times time required by Fred.
Time required by Ben =
Time required by Ben =
Hence Time required by Ben was 12 minutes.