how do you solve a^2-2a-3/a^2-9a+18 – a^2-5a-6/a^2+9a+8?
How do you solve the following expression:
(\frac{a^2 - 2a - 3}{a^2 - 9a + 18} - \frac{a^2 - 5a - 6}{a^2 + 9a + 8}?)
I would appreciate a detailed breakdown of the steps involved in simplifying this equation. Thank you!
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!
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