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

• 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

(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

(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