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Question Number 1260 by Rasheed Ahmad last updated on 18/Jul/15
What is degree of (x/y) ? (x and y are both variables)  Is (x/y)  and a constant of same degree?
$$\mathrm{What}\:\mathrm{is}\:\mathrm{degree}\:\mathrm{of}\:\frac{\mathrm{x}}{\mathrm{y}}\:?\:\left(\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{are}\:\mathrm{both}\:\mathrm{variables}\right) \\ $$$$\mathrm{Is}\:\frac{\mathrm{x}}{\mathrm{y}}\:\:\mathrm{and}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{same}\:\mathrm{degree}? \\ $$
Commented by prakash jain last updated on 18/Jul/15
Degree of rational expression is the degree  of N^r  or D^r  (higher of the two). A constant is of degree 0.  (1/x) is of degree 1.
$$\mathrm{Degree}\:\mathrm{of}\:\mathrm{rational}\:\mathrm{expression}\:\mathrm{is}\:\mathrm{the}\:\mathrm{degree} \\ $$$$\mathrm{of}\:\mathrm{N}^{\mathrm{r}} \:\mathrm{or}\:\mathrm{D}^{\mathrm{r}} \:\left(\mathrm{higher}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\right).\:\mathrm{A}\:\mathrm{constant}\:\mathrm{is}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{0}. \\ $$$$\frac{\mathrm{1}}{{x}}\:\mathrm{is}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{1}. \\ $$
Commented by prakash jain last updated on 18/Jul/15
(x/y) is not a polynomial.
$$\frac{{x}}{{y}}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{polynomial}.\: \\ $$
Commented by Rasheed Soomro last updated on 18/Jul/15
Is degree concerned only with polynmial? Couldn′t I say (1/x) is of  −1 degree?
$${Is}\:{degree}\:{concerned}\:{only}\:{with}\:{polynmial}?\:{Couldn}'{t}\:{I}\:{say}\:\frac{\mathrm{1}}{{x}}\:{is}\:{of} \\ $$$$−\mathrm{1}\:{degree}? \\ $$
Commented by Rasheed Ahmad last updated on 19/Jul/15
Thanks Sir  I didn′t know the cocept of degree  of rational expression before .
$${Thanks}\:{Sir} \\ $$$${I}\:{didn}'{t}\:{know}\:{the}\:{cocept}\:{of}\:{degree} \\ $$$${of}\:{rational}\:{expression}\:{before}\:. \\ $$

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