Answer:
1) x/2
2) 5/7
3) x + 3 / x + 5
4) 1/x + 3
5) x + 1
Explanation:
I'm assuming that the numbers right after the x's are the exponents of those x's since you didn't include the ^ symbol before the exponent number.
Steps for 1:
You can simplify the fraction 4/8 to 1/2. Now you have x³/2x². Next, simply the x's. When dividing variables of the same letter with exponents, subtract the bottom exponent from the top. In this case, it's 3 - 2 = 1. After dividing, move the x to the top. You are now left with x/2.
Steps for 2:
The first step is to factor both 5x + 20 and 7x + 28. To do this, find the greatest common factor (GCF) that you can take out for each. The GCF of 5x + 20 is 5, so you factor 5 out of 5x and 20. After doing so, for the numerator (the top), you're left with 5(x + 4).
Same thing for 7x + 28. The GCF is 7, so you factor 7 out of 7x and 28. After doing so, you're left with 7(x + 4) for the denominator (the bottom).
Now, your fraction should look like this: 5(x + 4) / 7(x + 4). Since x + 4 appears in the numerator and denominator, it cancels out (just cross both out). You're now left with 5/7.
Steps for 3:
Same steps from 2. First, factor 3x + 9. The GCF of 3x and 9 is 3, so factor 3 out of both. After doing so, you're left with 3(x + 3) for the numerator.
The GCF of 3x and 15 is also 3, so factor 3 out of both. After doing so, you're left with 3(x + 5) for the denominator. Your fraction now is 3(x + 3) / 3(x + 5). Since 3 appears on the top and bottom, it cancels out (just cross both out). You're now left with x + 3 / x + 5.
Steps for 4:
Similar steps as the ones above.
x - 3 can't be factored, but x² - 9 can be factored. After you factor x² - 9, your entire fraction is now x - 3 / (x + 3)(x - 3). Since x - 3 appears on the top and bottom, they cancel out (cross them out). You're now left with 1/x+3.
Steps for 5:
Similar steps as the ones above.
x - 1 can't be factored, but x² - 2x + 1 can be factored. After factoring, your entire fraction is now (x - 1)(x - 1) / x - 1. Since x - 1 appears on the top and bottom, they cancel out (cross them out). You're now left with the remaining x - 1.
Hope this helps!