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Question

Express 512+918÷512918 as an equivalent fraction with a rational denominator.

Solution
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To rationalise the denominator, which is equal to 512314, put 512=x and 314=y; then since x4y4=(xy)(x3+x2y+xy2+y4)
The required factor is 532+522.314+512.324+334;
and the rational denominator is 542344=523=22
the expression =(512+314)(532+522.314+512.324+334)22
=542+2.532.314+2.522324+2.512.324+34422
=14+532.314+5.312+512.32411

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