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1.) (x^2 - x - 6)/(x^2 - 4) Factorise the numerator: ((x + 2)(x - 3))/(x^2 - 4) Factorise the denominator (use difference of squares rule, (a+b)(a-b) = a^2 - b^2): ((x+2)(x-3))/((x+2)(x-2)) Cancel out like terms: (x-3)/(x-2) This is probably the answer to the question, because there are various solutions depending on which number greater than 0 x is. The reason that they give you x > 2 is so that they can avoid any confusion about what would happen is x = 2 in the denominator, because it's impossible to divide by zero. 2.) Easy... there are two ways to solve this: One: Divide 32 by 40. You now have one percent. Multiply by 100. 32/40 = 0.8 0.8 * 100 = 80 Two: Divide 100 by 40. Multiply by this 'ratio' of the current number to the whole number to find the whole number. 100/40 = 2.5 32 * 2.5 = 80 I prefer the first method, as it is easier to follow logically; however, the second is more common. 3.) This is simple. It wants 65% of 160, which is the same as saying (65/100) * 160, or 0.65 * 160. This is 104. If you want a method easier to use without a calculator, as above use 160/100 * 65, which amounts to the same thing. [=1.6*65 = 104]
If you're wondering how many games the team won, turn the word statement into an equation. The team won 65% of 160 games = .65 x 160. There's your answer.