5/x-2 - 4/x-3 express as a single fraction in its simplest form. I had done the question like this: = 5/x-2 (x-2)(x-3) -4/x-3 (x-2)(x-3) = 5x-15-4x+8 = x-7 but how in fraction?
just like in 5/6 - 3/7 you will need a common denominator.
In my example, it would be 42?
How did I get 42 ?
Next step
35/42 - 18/42 ---> how did I get those fractions
= 17/42
Now to your problem
5/(x-2) - 4(x-3)
LCD = (x-2)(x-3) ---> same step as above e.g
= 5(x-3)/((x-2)(x-3)) - 4(x-2)/((x-2)(x-3))
= (5x-15 -4x+8)/((x-2)(x-3))
= (x - 7)/((x-2)(x-3))
To express the expression 5/(x-2) - 4/(x-3) as a single fraction, you need to find a common denominator for the two fractions. In this case, the common denominator is (x-2)(x-3), as seen in your calculation.
Here's how you can combine the two fractions:
1. Multiply the numerator and denominator of the first fraction, 5/(x-2), by (x-3):
5/(x-2) * (x-3)/(x-3) = 5(x-3)/(x-2)(x-3)
This simplifies to: 5x-15/(x-2)(x-3)
2. Multiply the numerator and denominator of the second fraction, 4/(x-3), by (x-2):
4/(x-3) * (x-2)/(x-2) = 4(x-2)/(x-2)(x-3)
This simplifies to: 4x-8/(x-2)(x-3)
3. Now, you can combine the two fractions by subtracting the second fraction from the first:
(5x-15)/(x-2)(x-3) - (4x-8)/(x-2)(x-3)
To subtract fractions, you need a common denominator, which we already have. So, you keep the common denominator and subtract the numerators:
= (5x-15 - 4x+8)/(x-2)(x-3)
Simplifying the numerator:
= (x - 7)/(x-2)(x-3)
So, the expression 5/(x-2) - 4/(x-3) expressed as a single fraction in its simplest form is (x - 7)/(x-2)(x-3).