Question

I will give you a medal and become a fan if you help. I need step by step instructions.

Answer 1

simplify the complex fraction

Answer 2

step 1: make sure that both the denominator and numerator are expressed in the form of single rational number a/b form. here the denominator is sum of fractions. so add them by making them fractions with common denominator. it would be 2x (simply multiplying them both) and numerator would be x^3 + 4 (work backwards to verify)
step 2: after getting the fraction in the form of (a/b)/(c/d), use this formula for simplifying further
(a/b)/(c/d) = ad/bc. , here it would be {2x(3x-7)}/{(x^3 + 4)x^2}

Answer 3

But this doesnt really make sense

Answer 4

\[ \frac{ \frac{3x-7}{x^2} }{\frac{x^2}{2} + \frac{2}{x}} = \frac{\frac{3x-7}{x^2}}{\frac{xx^2 + 2\cdot2}{2x}} = \frac{\frac{3x-7}{x^2}}{\frac{x^3 + 4}{2x}} = \frac{3x-7}{x^2} \cdot \frac{2x}{x^3 + 4} = \\ = \frac{3x-7}{x} \cdot \frac{2}{x^3 + 4} = \frac{6x - 14}{x^4 + 4x} \]