Answer:
The simplest form is 2(3x - 7)/x(x³ + 4)
Step-by-step explanation:
* Lets revise how can divide fraction by fraction
- To simplify (a/b)/(c/d), change it to (a/b) ÷ (c/d)
∵ a/b ÷ c/d
- To solve it change the division sign to multiplication sign and
reciprocal the fraction after the sign
∴ a/b × d/c = ad/bc
* Now lets solve the problem
∵ [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{2}}{2}+\frac{2}{x}}[/tex]
- Lets take the denominator and simplify by make it a single
fraction, let the denominator of it 2x and change
the numerator
∴ [tex]\frac{x^{2}}{2}+\frac{2}{x}=\frac{x(x^{2})+2(2)}{(2)(x)}=\frac{x^{3}+4}{2x}[/tex]
∴ The fraction = [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+4}{2x}}[/tex]
* Now lets change it by (up ÷ down)
∴ [tex]\frac{3x-7}{x^{2}}[/tex] ÷ [tex]\frac{x^{3}+4}{2x}[/tex]
- Change the division sign to multiplication sign and reciprocal
the fraction after the sign
∴ [tex]\frac{3x-7}{x^{2}}[/tex] × [tex]\frac{2x}{x^{3}+4}[/tex]
∴ [tex]\frac{(2x)(3x-7)}{(x^{2})(x^{3}+4)}[/tex]
- We can simplify x up with x down
∴ [tex]\frac{2(3x-7)}{x(x^{3}+4)}[/tex]
* The simplest form is 2(3x - 7)/x(x³ + 4)
