Question

Simplify the complex fraction

Answer 1

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

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

- Lets take the denominator and simplify by make it a single

 fraction, let the denominator of it 2x and change

 the numerator

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

∴ The fraction = $\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+4}{2x}}$

* Now lets change it by (up ÷ down)

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

- Change the division sign to multiplication sign and reciprocal

 the fraction after the sign

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

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

- We can simplify x up with x down

∴ $\frac{2(3x-7)}{x(x^{3}+4)}$

* The simplest form is 2(3x - 7)/x(x³ + 4)