Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{3}{w^2x} - \frac{3w^3x}{4}$

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

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\frac{3}{w^2x} - \frac{3w^3x}{4}

Identify LCM: Identify the least common multiple (LCM) of the denominators $w^2x$ and $4$ . Since $w^2x$ and $4$ have no common factors other than $1$ , the LCM is simply their product, which is $4w^2x$ .
Convert fractions: Convert each fraction to have the LCM as the denominator. To do this, multiply the numerator and denominator of the first fraction by $4$ , and multiply the numerator and denominator of the second fraction by $w^2x$ . This gives us $(3\times 4)/(w^2x\times 4) - (3w^3x\times w^2x)/(4\times w^2x)$ .
Perform multiplication: Perform the multiplication in the numerators and denominators. This results in $\frac{12}{4w^2x} - \frac{3w^5x^2}{4w^2x}$ .
Simplify expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is $(12 - 3w^5x^2)/4w^2x$ .
Check for further simplification: Check if the numerator can be simplified further. Since there are no common factors between $12$ and $3w^5x^2$ , the expression is already in its simplest form.