What is \(\rm \frac{1}{x(x-y)(x-z)}+\frac{1}{y(y-z)(y-x)}+\frac{1}{z(z-x)(z-y)}\) equal to ?
\(\rm\frac{1}{xyz}\)
For nonzero, pairwise distinct x, y and z, combine over a common denominator:
Step 1:
\(\frac{yz(y-z)-xz(x-z)+xy(x-y)}{xyz(x-y)(x-z)(y-z)}\)
Step 2:
\(=\frac{(x-y)(x-z)(y-z)}{xyz(x-y)(x-z)(y-z)}=\frac1{xyz}\)
What is the value of \(\sqrt[3]{{4\frac{{12}}{{125}}}}\) ?
If \(\frac{{36}}{{11}} = 3\; + \;\frac{1}{{x\; + \;\frac{1}{{y\; + \;\frac{1}{z}}}}}\) , where x, y and z are natural numbers then what is (x + y + z) equal to?
What is \(\frac{{{6^2} + \;{7^2} + \;{8^2} + \;{9^2} + \;{{10}^2}}}{{\sqrt {7\; + \;4\sqrt 3 \;} - \;\sqrt {4\; + \;2\sqrt 3 } }}\) equal to?
In an examination, a student was asked to divide a certain number by 8. By mistake he multiplied it by 8 and got the answer 2016 more than the correct answer. What was the number?
What is \(\sqrt {1 + \frac{1}{{{1^{2}}}} + \frac{1}{{{2^{2}}}}} + \sqrt {1 + \frac{1}{{{2^{2}}}} + \frac{1}{{{3^{2}}}}} + \ldots \ldots .. + \sqrt {1 + \frac{1}{{{{2007}^{2}}}} + \frac{1}{{{{2008}^{2}}}}}\) equal to?
If \(x\, = \,7\, + \,4\sqrt 3 \) , then what is the value of \(\sqrt x \, + \,\frac{1}{{\sqrt x }}\) ?
If \(x + \frac{1}{{1 + \;\frac{1}{{2 + \;\frac{1}{3}}}}} = 2,\) then what is x equal to?
If \(\frac{{\rm{a}}}{{\rm{b}}} = \frac{1}{3},\frac{{\rm{b}}}{{\rm{c}}} = 2,\frac{{\rm{c}}}{{\rm{d}}} = \frac{1}{2},\frac{{\rm{d}}}{{\rm{e}}} = 3\) and \(\frac{{\rm{e}}}{{\rm{f}}} = \frac{1}{4}\) , then what is the value of \(\frac{{{\rm{abc}}}}{{{\rm{def}}}}?\)
Which one among the following is the largest?
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I | Column II | ||
a. | Equivalent fraction of \(\frac{7}{12}\) is | i. | Proper fraction |
b. | Equivalent fraction of \(\frac{9}{15}\) is | ii. | Improper fraction |
c. | \(\frac{7}{11}\) is | iii. | \(\frac{21}{36}\) |
d. | \(\frac{19}{5}\) is | iv. | \(\frac{3}{5}\) |
Among the fractions \(\frac{7}{12}\) , \(\frac{8}{15}\) , \(\frac{17}{24}\) and \(\frac{13}{18}\) , which is the smallest?