Find the illegal values of b in the fraction: 2b^2 + 3b - 10 over b^2 - 2b -8

The "illegal" (sometimes called "excluded") values of b are those values of b that would make the denominator equal zero. So, we set the denominator equal to zero and solve for b.

denominator = b² - 2b -8  ⇒⇒⇒ by factoring
∴ b² - 2b -8 = 0
   (b-4)(b+2) = 0
   b - 4 = 0     or  b + 2 = 0
∴ b = 4 or -2


the illegal values of b in the fraction = -2 , 4

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