A Text book of Algebra
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171 the equation to the other and combining two or more of them together, a considerable reduction may be effected and some long operations avoided.
294. As an instance take the equation 1 1 1 1 01 2~0 3 04 The L. C. M. Of the four denominators is (0 1) (02) (03) (04), and if the two equal expressions were at once multiplied by this L. C. M. , the reduction of the equation would involve the multiplication of three binomial factors for each original fraction. By combining the two fractions on ea...ch side into one, before proceeding to multiply, a much simpler process is required. The equation thus becomes (Art. 205) (0-2) -(0-1) _ (0-4)-(0-3) (0-1) (0-2) " (03) (0-4) -1 _ 1 (0-1) (0-2) "(0-3) (0-4)' Now, multiplying these equals by the L. C. M. Of their denominators, we obtain (0-1) (02) (0-3)(0 4) or _(0_3)(0_4) =(01) (02); (8) whence multiplying out, -02+ 70- 12 = -0 2 + 30-2; and transposing terms, as before, the two terms 2 disappear and we get 70-30 = 12-2, or 40 = 10 ; and by Axiom (4), 10 5 172 Simple Eqtiations [295.
What to read after A Text book of Algebra?
You can find similar books in the "Read Also" column, or choose other free books by W Steadman William Steadman Aldis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
171 the equation to the other and combining two or more of them together, a considerable reduction may be effected and some long operations avoided.
294. As an instance take the equation 1 1 1 1 01 2~0 3 04 The L. C. M. Of the four denominators is (0 1) (02) (03) (04), and if the two equal expressions were at once multiplied by this L. C. M. , the reduction of the equation would involve the multiplication of three binomial factors for each original fraction. By combining the two fractions on ea...ch side into one, before proceeding to multiply, a much simpler process is required. The equation thus becomes (Art. 205) (0-2) -(0-1) _ (0-4)-(0-3) (0-1) (0-2) " (03) (0-4) -1 _ 1 (0-1) (0-2) "(0-3) (0-4)' Now, multiplying these equals by the L. C. M. Of their denominators, we obtain (0-1) (02) (0-3)(0 4) or _(0_3)(0_4) =(01) (02); (8) whence multiplying out, -02+ 70- 12 = -0 2 + 30-2; and transposing terms, as before, the two terms 2 disappear and we get 70-30 = 12-2, or 40 = 10 ; and by Axiom (4), 10 5 172 Simple Eqtiations [295.
What to read after A Text book of Algebra?
You can find similar books in the "Read Also" column, or choose other free books by W Steadman William Steadman Aldis to read onlineMoreLess
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