Simplify. Assume that all variables result in nonzero denominators. Enter the expression in simplest form. The numerator and denominator must be in explanded form.

Simplify. Assume that all variables result in nonzero denominators.
Enter the expression in simplest form. The numerator and denominator must be in explanded form (i.e. not a product of factors).
$$\displaystyle\Rightarrow{\frac{{{6}{q}}}{{{q}+{1}}}}-{\frac{{{q}-{4}}}{{{q}}}}+{\frac{{{6}}}{{{q}+{1}}}}=$$

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$$\displaystyle\Rightarrow{\frac{{{6}{q}}}{{{q}+{1}}}}-{\frac{{{q}-{4}}}{{{q}}}}+{\frac{{{6}}}{{{q}+{1}}}}$$
$$\displaystyle\Rightarrow{\frac{{{6}{q}^{{{2}}}-{\left({q}-{4}\right)}{\left({q}+{1}\right)}+{6}{q}}}{{{q}{\left({q}+{1}\right)}}}}$$
$$\displaystyle\Rightarrow{\frac{{{6}{q}^{{{2}}}-{\left({q}^{{{2}}}+{q}-{4}{q}-{4}\right)}+{6}{q}}}{{{q}{\left({q}+{1}\right)}}}}$$
$$\displaystyle\Rightarrow{\frac{{{6}{q}^{{{2}}}-{\left({q}^{{{2}}}-{3}{q}-{4}\right)}+{6}{q}}}{{{q}{\left({q}+{1}\right)}}}}$$
$$\displaystyle\Rightarrow{\frac{{{6}{q}^{{{2}}}-{q}^{{{2}}}+{3}{q}+{4}+{6}{q}}}{{{q}{\left({q}+{1}\right)}}}}$$
$$\displaystyle\Rightarrow{\frac{{{5}{q}^{{{2}}}+{9}{q}+{4}}}{{{q}{\left({q}+{1}\right)}}}}$$
$$\displaystyle\Rightarrow{\frac{{{5}{q}^{{{2}}}+{5}{q}+{4}{q}+{4}}}{{{q}{\left({q}+{1}\right)}}}}$$
$$\displaystyle\Rightarrow{\frac{{{5}{q}{\left({q}+{1}\right)}+{4}{\left({q}+{1}\right)}}}{{{q}{\left({q}+{1}\right)}}}}$$
$$\displaystyle\Rightarrow{\frac{{{\left({5}{q}+{4}\right)}{\left({q}+{1}\right)}}}{{{q}{\left({q}+{1}\right)}}}}$$
$$\displaystyle\Rightarrow{\frac{{{5}{q}+{4}}}{{{q}}}}$$
So, the simplified expression is:
$$\displaystyle\Rightarrow{\frac{{{5}{q}+{4}}}{{{q}}}}$$