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The simplified form of the expression is \( \frac{15b^{3}+100ab^{2}-216a}{240ab^{3}} \).
Solución
Calculate or simplify the expression \( \frac{1}{16a}+\frac{5}{12b}-\frac{9}{10b^{3}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{1}{16a}+\frac{5}{12b}-\frac{9}{10b^{3}}\)
- step1: Reduce fractions to a common denominator:
\(\frac{3\times 5b\times b^{2}}{16a\times 3\times 5b\times b^{2}}+\frac{5\times 4\times 5ab^{2}}{12b\times 4\times 5ab^{2}}-\frac{9\times 6\times 4a}{10b^{3}\times 6\times 4a}\)
- step2: Multiply the terms:
\(\frac{3\times 5b\times b^{2}}{240ab\times b^{2}}+\frac{5\times 4\times 5ab^{2}}{12b\times 4\times 5ab^{2}}-\frac{9\times 6\times 4a}{10b^{3}\times 6\times 4a}\)
- step3: Multiply the terms:
\(\frac{3\times 5b\times b^{2}}{240ab\times b^{2}}+\frac{5\times 4\times 5ab^{2}}{240bab^{2}}-\frac{9\times 6\times 4a}{10b^{3}\times 6\times 4a}\)
- step4: Multiply the terms:
\(\frac{3\times 5b\times b^{2}}{240ab\times b^{2}}+\frac{5\times 4\times 5ab^{2}}{240bab^{2}}-\frac{9\times 6\times 4a}{240b^{3}a}\)
- step5: Multiply:
\(\frac{3\times 5b\times b^{2}}{240ab^{3}}+\frac{5\times 4\times 5ab^{2}}{240bab^{2}}-\frac{9\times 6\times 4a}{240b^{3}a}\)
- step6: Multiply:
\(\frac{3\times 5b\times b^{2}}{240ab^{3}}+\frac{5\times 4\times 5ab^{2}}{240b^{3}a}-\frac{9\times 6\times 4a}{240b^{3}a}\)
- step7: Rewrite the expression:
\(\frac{3\times 5b\times b^{2}}{240ab^{3}}+\frac{5\times 4\times 5ab^{2}}{240ab^{3}}-\frac{9\times 6\times 4a}{240ab^{3}}\)
- step8: Transform the expression:
\(\frac{3\times 5b\times b^{2}+5\times 4\times 5ab^{2}-9\times 6\times 4a}{240ab^{3}}\)
- step9: Multiply the terms:
\(\frac{15b^{3}+5\times 4\times 5ab^{2}-9\times 6\times 4a}{240ab^{3}}\)
- step10: Multiply the terms:
\(\frac{15b^{3}+100ab^{2}-9\times 6\times 4a}{240ab^{3}}\)
- step11: Multiply the terms:
\(\frac{15b^{3}+100ab^{2}-216a}{240ab^{3}}\)
The simplified form of the expression \( \frac{1}{16a}+\frac{5}{12b}-\frac{9}{10b^{3}} \) is \( \frac{15b^{3}+100ab^{2}-216a}{240ab^{3}} \).
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