How do you simplify $\frac{14 g^{3} h^{2}}{42 g h^{3}}$ $(14g^3h^2)/(42gh^3)$ and find the excluded values?

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Answer 1 · 2017-01-23T20:05:02

$\frac{14 g^{3} h^{2}}{42 g h^{3}} = \frac{g^{2}}{3 h}, h \neq 0$ $(14g^3h^2)/(42gh^3)=g^2/(3h), h !=0$

In order to simplify, we must remove the indices from the variables where they appear in the numerator and denominator.

$\frac{14}{42} = \frac{1}{3}$ $14/42=1/3$

We know that $\frac{a^{3}}{a^{2}} = a^{3 - 2} = a^{1} = a$ $a^3/a^2=a^(3-2)=a^1=a$ , so we can apply this to $g$ $g$ and $h$ $h$ in the fraction.

$\frac{g^{3}}{g} = g^{3 - 1} = g^{2}$ $g^3/g=g^(3-1)=g^2$

$\frac{h^{2}}{h^{3}} = h^{2 - 3} = h^{- 1} = \frac{1}{h}$ $h^2/h^3=h^(2-3)=h^-1=1/h$

We can now simplify the fraction:

$(1cancel(14)g^(2cancel(3))h^(-1cancel(2)))/(3cancel(42)cancel(g)cancel(h^3))=1/3g^2h^-1=g^2/(3h)$

Since this is a fraction, the denominator can't equal $0$ , so the only excluded value is $h=0$

How do you simplify (14g^3h^2)/(42gh^3)14g3h242gh3(14g^3h^2)/(42gh^3) and find the excluded values?