The function f is defined as f(x)=(7)/(2x^(2)-4x). Find f(x+6). Write your answer without parentheses, and simplify it as much as possible. f(x+6)= ◻

Substitute x with (x+6): Substitute x with (x+6) in the function f(x). We need to replace every instance of x in the function with (x+6). f(x+6) = (7)/(2(x+6)^2 - 4(x+6))Expand and distribute in denominator: Expand the squares and the multiplication in the denominator. We will expand (x+6)^2 and distribute the -4 across (x+6). f(x+6) = (7)/(2(x^2 + 12x + 36) - 4x - 24)Distribute and combine like terms: Distribute the 2 in the denominator and combine like terms. Multiply each term inside the parentheses by 2 and then subtract 4x and 24. f(x+6) = (7)/(2x^2 + 24x + 72 - 4x - 24)Combine like terms: Combine like terms in the denominator. Add or subtract the coefficients of like terms in the denominator. f(x+6) = (7)/(2x^2 + 20x + 48)Check for simplification: Check for any further simplification. The expression (7)/(2x^2 + 20x + 48) is already in its simplest form. There are no common factors to reduce the fraction further.

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The function $f$ is defined as $f(x)=\frac{7}{2x^{2}-4x}$ . $\newline$ Find $f(x+6)$ . $\newline$ Write your answer without parentheses, and simplify it as much as possible. $\newline$ $f(x+6)=$ $\square$

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Q. The function

f

is defined as

f(x)=\frac{7}{2x^{2}-4x}

\newline

Find

f(x+6)

\newline

Write your answer without parentheses, and simplify it as much as possible.

\newline

f(x+6)=

\square

Substitute $x$ with $(x+6)$ : Substitute $x$ with $(x+6)$ in the function $f(x)$ . We need to replace every instance of $x$ in the function with $(x+6)$ . $f(x+6) = \frac{7}{2(x+6)^2 - 4(x+6)}$
Expand and distribute in denominator: Expand the squares and the multiplication in the denominator. $\newline$ We will expand $(x+6)^2$ and distribute the $-4$ across $(x+6)$ . $\newline$ $f(x+6) = \frac{7}{2(x^2 + 12x + 36) - 4x - 24}$
Distribute and combine like terms: Distribute the $2$ in the denominator and combine like terms. $\newline$ Multiply each term inside the parentheses by $2$ and then subtract $4x$ and $24$ . $\newline$ $f(x+6) = \frac{7}{2x^2 + 24x + 72 - 4x - 24}$
Combine like terms: Combine like terms in the denominator. $\newline$ Add or subtract the coefficients of like terms in the denominator. $\newline$ $f(x+6) = \frac{7}{2x^2 + 20x + 48}$
Check for simplification: Check for any further simplification. $\newline$ The expression $(7)/(2x^2 + 20x + 48)$ is already in its simplest form. There are no common factors to reduce the fraction further.