How many right-angled triangles are in the seven-piece Chinese tangram?

X / (x² - 6x + 9) + 3/(x² + x - 12) - x/(x² + x - 12) Just like any other addition/subtraction of fractions problem, you need to find a common denominator. So to find the LCD, we need to factor the denominators that we have: x / (x - 3)² + 3/(x + 4)(x - 3) - x/(x + 4)(x - 3) Do the LCD is: (x + 4)(x - 3)² To get a common denominator, multiply the first fraction by (x + 4)/(x + 4) and the other two fractions by (x - 3)/(x - 3). Now we have: x(x + 4) / (x + 4)(x - 3)² + 3(x - 3)/(x + 4)(x - 3)² - x(x - 3)/(x + 4)(x - 3)² Now that we have all denominators the same, we can now add/subtract the numerators.

That gives us: x(x + 4) + 3(x - 3) - x(x - 3) / (x + 4)(x - 3)² Now simplify the numerator and re-factor, if we can, to see if we have any common factors with the denominator. (x² + 4x + 3x - 9 - x² + 3x) / (x + 4)(x - 3)² (10x - 9) / (x + 4)(x - 3)² No common factors, so now we can expand the denominator to get our final answer: (10x - 9) / (x + 4)(x² - 6x + 9) (10x - 9) / (x³ - 6x² + 9x + 4x² - 24x + 36) (10x - 9) / (x³ - 2x² - 15x + 36) That is your reduced and simplified form of the solution.

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