You have to find the LCD or least common denominator.
In this case the LCD would be (x-6)(x+5).
Problem: x/ x-6 - 1/x+5
Step 1: multiply x-6 to the numerator and denominator of 1/x+5
1(x-6)/ (x+5)(x-6)
Step 2: multiply x+5 to the numerator and denominator of x/x-6
x(x+5)/ (x+5)(x-6)
After all that, this is how the problem should look now
x(x+5)/ (x-6)(x+5) - 1(x-6)/ (x-6)(x+5)
If you simplify this you get
x²+5x-x+6/ (x-6)(x+5)
If you subtract both 5x-x (like terms) you get
x²+4x+6/ (x-6)(x+5)
which is the answer
Any real number line ranges from negative infinity to positive infinity. A real number number line consists of all the rational and irrational numbers. Let us take three intervals which contain both the rational and irrational numbers.
First interval: [3,4]
Since every integer is a rational number, 3 and 4 are both rational. In this interval there occurs the value of π (3.14159..) which is an irrational number.
Second interval : [0,2]
0 and 2 are integers and hence are rational. In this interval, occurs √2 (1.41421...) is an irrational number.
Third interval : [2,3]
In this interval, Eulers number 'e' lie whose value is (2.718281.. )
Hence we can conclude that, there occurs an irrational number between any two rational number.
Are you sure that the question?
First, we add everything together, so; 3 + 3 + 4 + 2 = 12. This means every marble has a 8.33% chance of being chosen, however since there are more than others we add those separate percentages together.
Pink: 25%
Violet: 25%
Yellow: 33.33%
Brown: 16.66%
These are the chances of you getting either color. Since the problem asks what is the probability of finding a violet marble,we just look at the written percentages to see we have a 25% chance of choosing a violet marble.
The next step is to see what is the probability of choosing a pink marble, except we have to change things up a bit. Since we removed 1 marble, that changes ALL the percentages again, so we must rewrite the percentages. 12 - 1 is easily solved as 11, and so this means every marble has a 9.0909091% of being chosen. Let's rewrite the grouped percentages now:
Pink: 27.27%
Violet: 18.18%
Yellow: 36.36%
Brown: 18.18%
Now we see that with one marble removed, and that marble not being pink, we have a 27.27% chance of picking a pink marble.
Your Answer: 25% of Violet first time, 27.27% of Pink second time.
(How To Get Percentages?): Simple, you divide 100 (since whatever number we start out with as long as it claims nothing is missing equal 100%) by whatever number of objects you have. So as an example, if I have 5 objects, 100 / 5 = 20. This means every individual object has a 20% chance of being chosen. But we then arrange everything into whatever groups (in your problems case, colors) and multiply by the amount. So say I have 3 green balls and 2 white balls, 3 x 20 = 60 and 2 x 20 = 40 so I have a 60% of getting a green ball and 40% chance of a white ball.
Hope this helps and I hope even more you learned something :D
