Simplify into one fraction. -4x/x+7-8/x+7

A. -4x+8/x+7
B. X-8/x
C. -4x-8/x+7
D. X+7/-4x**

Simplify into one fraction. -2/x+3-4/x-5
A. -6x-2/(x+3)(x-5)
B. 6(x-1)/(x+3)(x-5)
C. -6/(x+3)(x-5) ***
D. 2/(x+3)(x-5)

since the denominators are the same, just add numerators. Just as

2/5 + 1/5 = 3/5,

-4x/(x+7) - 8/(x+7) = (-4x-8)/(x+7)
So, C

-2/(x+3) - 4/(x-5)
= [-2(x-5) - 4(x+3)]/[(x+3)(x-5)
= (-2x+10-4X-12)/[(x+3)(x-5)
= (-6x-2)/[(x+3)(x-5)
So, A

D. X+7/-4x

To simplify the expression -4x/(x+7) - 8/(x+7), you need to find a common denominator for the fractions and then combine them.

Step 1: Find the common denominator.
In this case, the common denominator is (x+7) because both fractions have (x+7) as their denominators.

Step 2: Rewrite the fractions with the common denominator.
The first fraction -4x/(x+7) remains as it is since it already has the common denominator.

The second fraction 8/(x+7) needs to be multiplied by (x+7)/(x+7) to have the common denominator:
8/(x+7) * (x+7)/(x+7) = 8(x+7)/(x+7)^2

Step 3: Combine the fractions.
Now that both fractions have the same denominator, you can subtract them:
-4x/(x+7) - 8(x+7)/(x+7)^2

Step 4: Simplify the expression.
To simplify further, you can factor out a common factor of -4 from the numerator:
-4(x)/(x+7) - 8(x+7)/(x+7)^2

Now, you can combine the numerators over the common denominator:
(-4x - 8(x+7))/(x+7)^2

Simplifying the numerator:
(-4x - 8x - 56)/(x+7)^2
(-12x - 56)/(x+7)^2

Therefore, the simplified expression is (-12x - 56)/(x+7)^2.

To simplify the expressions into one fraction, you need to find a common denominator for both fractions in each expression.

Let's start with the first expression: -4x/(x+7) - 8/(x+7)

Step 1: Find the common denominator
In this case, the common denominator is (x+7) since both fractions have (x+7) in their denominators.

Step 2: Combine the fractions
To combine the fractions, we need to have the same denominator. Multiply the first fraction by (x+7)/(x+7) and the second fraction by -4x/(4x).

-4x/(x+7) - 8/(x+7) = (-4x(x+7))/(x+7)^2 - 8(-4x)/(4x(x+7))

Step 3: Simplify
Simplify the numerators in the combined fraction and put them over the common denominator.

= (-4x^2 - 28x - 32x)/(x+7)^2

= (-4x^2 - 60x)/(x+7)^2

Now, let's move on to the second expression: -2/(x+3) - 4/(x-5)

Step 1: Find the common denominator
In this case, the common denominator is (x+3)(x-5) since both fractions have (x+3) and (x-5) in their denominators.

Step 2: Combine the fractions
To combine the fractions, we need to have the same denominator. Multiply the first fraction by (x-5)/(x-5) and the second fraction by -2/(2).

-2/(x+3) - 4/(x-5) = -2(x-5)/((x+3)(x-5)) - 4(-2)/2((x+3)(x-5))

Step 3: Simplify
Simplify the numerators in the combined fraction and put them over the common denominator.

= (-2x+10)/((x+3)(x-5)) + 8/((x+3)(x-5))

= (-2x+10 + 8)/((x+3)(x-5))

= (-2x+18)/((x+3)(x-5))

Therefore, the simplified expressions are:
A. -4x+8/(x+7)
C. -4x-8/(x+7)

For the second expression:
C. -6/(x+3)(x-5)