...parenthesis is positive. 3. If after this, either or both of the exponents of x should be fractional, we can substitute for x another variable, with an exponent...multiple of the denominators of the given exponents, and thus get rid of the fractions, as in the example ~" by making ж = z', we obtain x^dx^a ~b ox )q...

...should be fractional, cither within or without the parenthesis, or both, \\o can substitute for .r another variable, with an exponent equal to the least...multiple of the denominators of the given exponents, and thus get rid of the fractions, as in the example by making x = z", we obtain x"dx(a + ba^)"r in...

...reduced to the form M which the exponents m and n are whole numbers, and n is positive. 1st. For if 77i and n were fractional, and the binomial were of the...were negative, or the expression were of the form in which the exponent of the variable within the parenthesis is positive. 3d. If the variable x were...

...free the equation of fractional exponents, substitute for the unknown quantity a new unknown quantity with an exponent equal to the least common multiple of the denominators of the exponents in the equation. Thus, in (1) mf put y = z"', whence y" = z™, y ' = г"' , and у' = г1"'....

...positive and x enters but one term of the binomial. For if m and n are fractional we may substitute another variable with an exponent equal to the least...multiple of the denominators of the given exponents, which will then be reducible to whole numbers. If, for example, we have we make x=z6, then dx=bz^dz,...

...positive and x enters but one term of the binomial. For if m and « are fractional we may substitute another variable with an exponent equal to the least...multiple of the denominators of the given exponents, which will then be reducible to whole numbers. If, for example, we have 1 1 P. we make j:=26,then dx=62*dz,...

...free the equation of fractional exponents, substitute for the unknown quantity a new unknown quantity with an exponent equal to the least common multiple of the denominators of the exponents in the equation. Thus, in (1) mr put y = г" , whence у " — z"" , у' — г", and y'...

...free the equation of fractional exponents, substitute for the unknown quantity a new unknown quantity with an exponent equal to the least common multiple of the denominators of the exponents in the equation. Thus, in (1) put у =: г", whence у* = z"*, у' = z°r, and y1 — e"*1....

...free the equation of fractional exponents, substitute for the unknown quantity a new unknown quantity with an exponent equal to the least common multiple of the denominators of the exponents in the equation. Thus, in (1) put y = z", whence y * — z"", y ' = e", and y' = z"". These...

...function containing only monomial surds may be rationalized by substituting for the variable a new variable with an exponent equal to the least common multiple of the denominators of the fractional exponents in the function. For example, to find j 5- dx. J 1 + ж* Assume x = z6 ; then...