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Question

Evaluate: limx1x+88x+15x7x3

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Solution

Method of rationalising both numerators and denominators,
=limx1(x+88x+1)(5x+7x3)(5x7x3)(5x+7x3)
=limx1((x+8)8x+1)(5x+7x3)5x7x+3
=limx1(x+88x+1)(5x+7x3)8x+8×x+8+8x+1x+8+8x+1
=limx1(x+88x+1)(5x+7x3)(x+8+8x+1)8(x1)((x+8+8x+1))
=limx1(x+88x1)(5x+7x3)8(x1)((x+8+8x+1))
=limx1(7x+7)(5x+7x3)8(x1)(x+8+8x+1)
=limx17(x1)(5x+7x3)8(x1)(x+8+8x+1)
=limx17(5x+7x3)8(x+8+8x+1)
=7(51+7×13)8(1+8+8×1+1)
=7(4+4)8(9+9)
=144169
=14×216×3
=74×3
=712








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