Simplify into one fraction. Fraction 1: 8 times x over the quantity x minus 8; Fraction 2: 2 over the quantity x minus 8. Find Fraction 1 minus Fraction 2.

Question

A. The quantity 8 times x plus 2 over the quantity x minus 8
B. The quantity 8 times x minus 2 over the quantity x minus 8
C. The quantity 8 times x plus 2 over the quantity x minus 8 squared
D. The quantity 8 times x minus 2 over the quantity x minus 8 squared

Answer 1

To simplify Fraction 1, we can first factor out an x from the numerator:

$$\frac{8x}{x-8}=\frac{x\cdot 8}{x-8}=\frac{8x}{x-8}$$

To subtract Fraction 2, we need a common denominator of (x-8):

$$\frac{2}{x-8}=\frac{2\cdot 1}{x-8}$$

Subtracting, we get:

$$\frac{8x}{x-8}-\frac{2}{x-8}=\frac{8x-2}{x-8}$$

Simplifying the numerator:

$$8x-2=2(4x-1)$$

So the final answer is:

$$\boxed{\textbf{(B) } \frac{8x-2}{x-8}}$$

Answer 2

can you choose one of the multiple choice answers

Answer 3

Sorry, I forgot to select one of the multiple choice answers. The correct answer is:

$$\boxed{\textbf{(B) } \frac{8x-2}{x-8}}$$

Answer 4

Simplify into one fraction.
Fraction 1: 6 over the quantity x plus 7; Fraction 2: 3 over the quantity x minus 2. Find Fraction 1 minus Fraction 2.
A. Start Fraction 3 left-parenthesis lower x minus 33 right-parenthesis over left-parenthesis lower x plus 7 right-parenthesis left-parenthesis lower x minus 2 right-parenthesis End Fraction
B. 3 times the quantity x minus 11 over the quantity x plus 7 times the quantity x minus 2
C. 3 over the quantity x plus 7 times the quantity x minus 2
D. 9 over the quantity x plus 7 times the quantity x minus 2

Answer 5

To simplify Fraction 1, we can leave it as it is. To simplify Fraction 2, we can leave the denominator as it is and multiply the numerator by $\frac{x+7}{x+7}$ to obtain:

$$\frac{3(x+7)}{(x+7)(x-2)}=\frac{3x+21}{x^2+5x-14}$$

Subtracting the two fractions, we get:

$$\frac{6}{x+7}-\frac{3x+21}{x^2+5x-14}$$

To combine the two fractions, we need a common denominator of $(x+7)(x-2)$:

$$\frac{6(x-2)}{(x+7)(x-2)}-\frac{3x+21}{(x+7)(x-2)}$$

Simplifying the numerator:

$$6(x-2)-(3x+21)=3x-33$$

So the final answer is:

$$\boxed{\textbf{(A) } \frac{3(x-33)}{(x+7)(x-2)}}$$