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.
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
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:
$$\boxed{\textbf{(B) } \frac{8x-2}{x-8}}$$
can you choose one of the multiple choice answers
Sorry, I forgot to select one of the multiple choice answers. The correct answer is:
$$\boxed{\textbf{(B) } \frac{8x-2}{x-8}}$$
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
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:
$$\boxed{\textbf{(A) } \frac{3(x-33)}{(x+7)(x-2)}}$$
To simplify Fraction 1:
8 times x over the quantity x minus 8 can be written as (8x)/(x - 8).
To simplify Fraction 2:
2 over the quantity x minus 8 can be written as 2/(x - 8).
To find Fraction 1 minus Fraction 2, we need to subtract the two fractions:
(8x)/(x - 8) - 2/(x - 8)
To subtract fractions with the same denominator, we keep the denominator the same and subtract the numerators:
(8x - 2)/(x - 8)
Therefore, Fraction 1 minus Fraction 2 simplifies to (8x - 2)/(x - 8).
The correct answer is D. The quantity 8 times x minus 2 over the quantity x minus 8 squared.
To simplify the given fractions, Fraction 1: 8x/(x-8) and Fraction 2: 2/(x-8), we need to find a common denominator and combine the fractions.
The common denominator is (x-8), so we need to rewrite both fractions with this denominator.
For Fraction 1: 8x/(x-8), we already have the common denominator.
For Fraction 2: 2/(x-8), we can multiply both the numerator and denominator by (x-8) to get the common denominator: 2(x-8)/(x-8).
Now, let's combine the fractions:
Fraction 1 minus Fraction 2 is equal to (8x/(x-8)) - (2(x-8)/(x-8)).
Next, simplify the expression:
= (8x - 2(x-8))/(x-8)
= (8x - 2x + 16)/(x-8)
= (6x + 16)/(x-8)
Therefore, the simplified form of Fraction 1 minus Fraction 2 is (6x + 16)/(x-8).
The correct answer is A. The quantity 8 times x plus 2 over the quantity x minus 8.