how do you solve a^2-2a-3/a^2-9a+18 – a^2-5a-6/a^2+9a+8?

4 Answers

  • Hi,

    a² – 2a – 3 . . . a² – 5a – 6

    —————– – —————– =

    a² – 9a + 18. . a² + 9a + 8

    (a – 3)(a + 1) . (a – 6)(a + 1)

    —————– – ——————– =

    (a – 6)(a – 3). . (a + 8)(a + 1)

    a + 1 . a – 6

    ——– – ——– =

    a – 6. . a + 8

    (a + 1)(a + 8) . (a – 6)(a – 6)

    ——————– – —————— =

    (a – 6)(a + 8). . (a + 8)(a – 6)

    a² + 9a + 8 . . . a² – 12a + 36

    ——————- – ——————– =

    (a – 6)(a + 8) . . (a – 6)(a + 8)

    a² + 9a + 8 – (a² – 12a + 36)

    —————————————- =

    (a – 6)(a + 8)

    a² + 9a + 8 – a² + 12a – 36

    ————————————– =

    (a – 6)(a + 8)

    21a – 28

    ——————- <==ANSWER

    (a – 6)(a + 8)

    I hope that helps!! 🙂

  • a² – 2a – 3 . . . a² – 5a – 6

    —————– – —————– =

    a² – 9a + 18. . a² + 9a + 8

    (a – 3)(a + 1) . (a – 6)(a + 1)

    —————– – ——————– =

    (a – 6)(a – 3). . (a + 8)(a + 1)

    a + 1 . a – 6

    ——– – ——– =

    a – 6. . a + 8

    (a + 1)(a + 8) . (a – 6)(a – 6)

    ——————– – —————— =

    (a – 6)(a + 8). . (a + 8)(a – 6)

    a² + 9a + 8 . . . a² – 12a + 36

    ——————- – ——————– =

    (a – 6)(a + 8) . . (a – 6)(a + 8)

    a² + 9a + 8 – (a² – 12a + 36)

    ————————————–… =

    (a – 6)(a + 8)

    a² + 9a + 8 – a² + 12a – 36

    ————————————– =

    (a – 6)(a + 8)

    21a – 28

    ——————- <==ANSWER

    (a – 6)(a + 8)

  • ✐Explanation✐

    Factor.

    (a – 3)(a + 1)/[(a – 6)(a – 3)] – (a – 6)(a + 1)/[(a + 8)(a + 1)]

    Determine the LCD for the equation and have both fractions contain same denominator.

    LCD = (a – 6)(a – 3)(a + 8)(a + 1)

    You get:

    [(a – 3)(a + 1)²(a + 8)]/[(a – 6)(a – 3)(a + 8)(a + 1)] – [(a – 6)²(a + 1)(a – 3)]/[(a – 6)(a – 3)(a + 8)(a + 1)]

    You evaluate the equation above by yourself. Combine the numerator altogether and simplify the equation!

    I hope that helps!

    Source(s): Knowledge
  • what i would do is collect like terms.

    a^2-2a-3/a^2-9a+18-a^2-5a-6/a^2+9a+8

    =a^2-a^2-3/a^2-6/a^2-2a-5a+18+8

    =-9/a^2-7a+26

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