Question

Simplify the complex fraction

Answer 1

Answer:

$\frac{6x-14}{x^{4} +4x}$

Step-by-step explanation:

I have to $\frac{\frac{3x-7}{x^{2} } }{\frac{x^{2} }{2}+\frac{2}{x}}$

Let's start by joining the macro denominator with a common denominator. So, by applying a minimum common multiple $\frac{x^{2} }{2} +\frac{2}{x}=\frac{x^{3}+ 4 }{2x}$

Now I can write the expression as

$\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+ 4 }{2x}}$

Now to convert both fractions into one, I multiply the numerator of the one above by the denominator of the one below, and the denominator of the one above with the numerator below, remaining that way.

$\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+4}{2x}}=\frac{(3x-7)(2x)}{(x^{2})(x^{3}+ 4)}$

Having the fraction in this way, I could simplify the x of the "2x" of the numerator with an x^2 (x^2=x*x) of the denominator

$\frac{(3x-7)(2x)}{(x^{2})(x^{3}+4)}=\frac{2(3x-7)}{x(x^{3}+ 4)}$

finally, applying distributive property, I have to

$\frac{(6x-14)}{(x^{4}+ 4x)}$

Done