Questions: (a) Write 4x^2+33x as a fraction. (b) What is the reciprocal of 4x^2+33x?

$(a) Write 4x^2+33x as a fraction. (b) What is the reciprocal of 4x^2+33x?$

Transcript text: (a) Write $4 x^{2}+33 x$ as a fraction. (b) What is the reciprocal of $4 x^{2}+33 x$ ?

Solution

Solution Steps

Solution Approach

(a) To write $4x^2 + 33x$ as a fraction, we can simply place it over 1, since any expression can be written as a fraction with a denominator of 1.

(b) The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For the expression $4x^2 + 33x$, which we wrote as $\frac{4x^2 + 33x}{1}$, the reciprocal would be $\frac{1}{4x^2 + 33x}$.

Step 1: Writing the Expression as a Fraction

The expression $4x^2 + 33x$ can be written as a fraction by placing it over 1. Thus, we have: \[ \frac{4x^2 + 33x}{1} \]

Step 2: Finding the Reciprocal

The reciprocal of the expression $4x^2 + 33x$ is obtained by swapping the numerator and the denominator. Therefore, the reciprocal is: \[ \frac{1}{4x^2 + 33x} \]