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JAMB 1986 · UME · Q22

Simplify 15x+5+17x+7\dfrac{1}{5x + 5} + \dfrac{1}{7x + 7}.

Worked solution (try it first)
  1. Factorise each bottom: 5x+5=5(x+1)5x + 5 = 5(x + 1) and 7x+7=7(x+1)7x + 7 = 7(x + 1).
  2. The LCD is 35(x+1)35(x + 1).
  3. Multiply the first top by 7 and the second by 5: 7+535(x+1)\frac{7 + 5}{35(x + 1)}.
  4. So the sum is 1235(x+1)=1235x+35\dfrac{12}{35(x + 1)} = \dfrac{12}{35x + 35}, option D.

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