Notes: `(16/(x-2))/(4/(x+1)+6/x)` Simplify the complex fraction.

Wednesday, 10 June 2015

$\displaystyle\frac{{\frac{{16}}{{{x}-{2}}}}}{{\frac{{4}}{{{x}+{1}}}+\frac{{6}}{{x}}}}$ Simplify the complex fraction.

To simplify the given complex fraction $\displaystyle\frac{{\frac{{16}}{{{x}-{2}}}}}{{\frac{{4}}{{{x}+{1}}}+\frac{{6}}{{x}}}}$ , we may look for the LCD or least common denominator.

The denominators are $\displaystyle{\left({x}-{2}\right)}$ , $\displaystyle{x}$ , and $\displaystyle{\left({x}+{1}\right)}$ . All are distinct factors.

Thus, we get the LCD by getting the product of the distinct factors from denominator side of each term.

$\displaystyle{L}{C}{D}={\left({x}-{2}\right)}\cdot{x}\cdot{\left({x}+{1}\right)}$

Maintain the factored form of the LCD for easier cancellation of common factors on each term.

Multiply each term by the...

To simplify the given complex fraction $\displaystyle\frac{{\frac{{16}}{{{x}-{2}}}}}{{\frac{{4}}{{{x}+{1}}}+\frac{{6}}{{x}}}}$ , we may look for the LCD or least common denominator.

The denominators are $\displaystyle{\left({x}-{2}\right)}$ , $\displaystyle{x}$ , and $\displaystyle{\left({x}+{1}\right)}$ . All are distinct factors.

Thus, we get the LCD by getting the product of the distinct factors from denominator side of each term.

$\displaystyle{L}{C}{D}={\left({x}-{2}\right)}\cdot{x}\cdot{\left({x}+{1}\right)}$

Maintain the factored form of the LCD for easier cancellation of common factors on each term.

Multiply each term by the LCD=(x-2)*x* (x+1).

$\displaystyle\frac{{\frac{{16}}{{{x}-{2}}}\cdot{\left({x}-{2}\right)}\cdot{x}\cdot{\left({x}+{1}\right)}}}{{\frac{{4}}{{{x}+{1}}}\cdot{\left({x}-{2}\right)}\cdot{x}\cdot{\left({x}+{1}\right)}+\frac{{6}}{{x}}\cdot{\left({x}-{2}\right)}\cdot{x}\cdot{\left({x}+{1}\right)}}}$

$\displaystyle\frac{{{16}\cdot{x}\cdot{\left({x}+{1}\right)}}}{{{4}\cdot{\left({x}-{2}\right)}\cdot{x}+{6}\cdot{\left({x}-{2}\right)}\cdot{\left({x}+{1}\right)}}}$

Apply distributive property.

$\displaystyle\frac{{{16}{x}\cdot{\left({x}+{1}\right)}}}{{{\left({4}{x}-{8}\right)}\cdot{x}+{\left({6}{x}-{12}\right)}\cdot{\left({x}+{1}\right)}}}$

$\displaystyle\frac{{{16}{{x}}^{{2}}+{16}{x}}}{{{\left({4}{{x}}^{{2}}-{8}{x}\right)}+{\left({6}{{x}}^{{2}}+{6}{x}-{12}{x}-{12}\right)}}}$

Combine possible like terms.

$\displaystyle\frac{{{16}{{x}}^{{2}}+{16}{x}}}{{{\left({4}{{x}}^{{2}}-{8}{x}\right)}+{\left({6}{{x}}^{{2}}-{6}{x}-{12}\right)}}}$

$\displaystyle\frac{{{16}{{x}}^{{2}}+{16}{x}}}{{{4}{{x}}^{{2}}-{8}{x}+{6}{{x}}^{{2}}-{6}{x}-{12}}}$

$\displaystyle\frac{{{16}{{x}}^{{2}}+{16}{x}}}{{{10}{{x}}^{{2}}-{14}{x}-{12}}}$

Factor out 2 from each side.

$\displaystyle\frac{{{2}{\left({8}{{x}}^{{2}}+{8}{x}\right)}}}{{{2}{\left({5}{{x}}^{{2}}-{7}{x}-{6}\right)}}}$

Cancel out common factor $\displaystyle{2}$ .

$\displaystyle\frac{{{8}{{x}}^{{2}}+{8}{x}}}{{{5}{{x}}^{{2}}-{7}{x}-{6}}}$

The complex fraction $\displaystyle\frac{{\frac{{16}}{{{x}-{2}}}}}{{\frac{{4}}{{{x}+{1}}}+\frac{{6}}{{x}}}}$ simplifies to $\displaystyle\frac{{{8}{{x}}^{{2}}+{8}{x}}}{{{5}{{x}}^{{2}}-{7}{x}-{6}}}$ .

Notes

Wednesday, 10 June 2015

$\displaystyle\frac{{\frac{{16}}{{{x}-{2}}}}}{{\frac{{4}}{{{x}+{1}}}+\frac{{6}}{{x}}}}$ Simplify the complex fraction.

No comments:

Post a Comment

How are race, gender, and class addressed in Oliver Optic's Rich and Humble?

Wednesday, 10 June 2015

Simplify the complex fraction.

No comments:

Post a Comment

How are race, gender, and class addressed in Oliver Optic&#39;s Rich and Humble?

$\displaystyle\frac{{\frac{{16}}{{{x}-{2}}}}}{{\frac{{4}}{{{x}+{1}}}+\frac{{6}}{{x}}}}$ Simplify the complex fraction.

How are race, gender, and class addressed in Oliver Optic's Rich and Humble?