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

This encounters adding, subtracting and finding the least usual multiple.

You are watching: Simplify the difference a^2-2a-3

## Step by step Solution ## Step 1 :

a2 - 5a - 6 simplify ——————————— a2 + 9a + 8Trying to element by dividing the middle term1.1Factoring a2 - 5a - 6 The first term is, a2 the coefficient is 1.The center term is, -5a that coefficient is -5.The last term, "the constant", is -6Step-1 : multiply the coefficient that the an initial term by the constant 1•-6=-6Step-2 : uncover two determinants of -6 whose sum equates to the coefficient of the center term, i beg your pardon is -5.

 -6 + 1 = -5 That"s it

Step-3 : Rewrite the polynomial dividing the middle term utilizing the two components found in step2above, -6 and 1a2 - 6a+1a - 6Step-4 : include up the an initial 2 terms, pulling out choose factors:a•(a-6) add up the critical 2 terms, pulling out typical factors:1•(a-6) Step-5:Add up the four terms of step4:(a+1)•(a-6)Which is the preferred factorization

Trying to aspect by dividing the middle term

1.2Factoring a2+9a+8 The an initial term is, a2 its coefficient is 1.The center term is, +9a its coefficient is 9.The last term, "the constant", is +8Step-1 : main point the coefficient that the first term through the continuous 1•8=8Step-2 : uncover two determinants of 8 whose sum equates to the coefficient the the center term, i beg your pardon is 9.

 -8 + -1 = -9 -4 + -2 = -6 -2 + -4 = -6 -1 + -8 = -9 1 + 8 = 9 That"s it

Step-3 : Rewrite the polynomial separating the middle term using the two factors found in step2above, 1 and 8a2 + 1a+8a + 8Step-4 : add up the an initial 2 terms, pulling out prefer factors:a•(a+1) include up the critical 2 terms, pulling out usual factors:8•(a+1) Step-5:Add increase the four terms of step4:(a+8)•(a+1)Which is the wanted factorization

Canceling the end :

1.3 Cancel the end (a+1) which appears on both political parties of the portion line.

Equation in ~ the end of step 1 :

(((a2)-2a)-3) (a-6) ——————————————-————— (((a2)-9a)+18) a+8

## Step 2 :

a2 - 2a - 3 simplify ———————————— a2 - 9a + 18Trying to factor by separating the center term2.1Factoring a2 - 2a - 3 The first term is, a2 that is coefficient is 1.The middle term is, -2a that coefficient is -2.The critical term, "the constant", is -3Step-1 : multiply the coefficient that the an initial term through the constant 1•-3=-3Step-2 : find two components of -3 whose sum amounts to the coefficient the the center term, i m sorry is -2.

 -3 + 1 = -2 That"s it

Step-3 : Rewrite the polynomial dividing the middle term using the two factors found in step2above, -3 and also 1a2 - 3a+1a - 3Step-4 : include up the an initial 2 terms, pulling out favor factors:a•(a-3) include up the critical 2 terms, pulling out typical factors:1•(a-3) Step-5:Add increase the four terms the step4:(a+1)•(a-3)Which is the preferred factorization

Trying to aspect by splitting the middle term

2.2Factoring a2-9a+18 The first term is, a2 that coefficient is 1.The middle term is, -9a that is coefficient is -9.The last term, "the constant", is +18Step-1 : main point the coefficient that the first term through the continuous 1•18=18Step-2 : discover two components of 18 whose sum equals the coefficient that the center term, which is -9.

 -18 + -1 = -19 -9 + -2 = -11 -6 + -3 = -9 That"s it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step2above, -6 and also -3a2 - 6a-3a - 18Step-4 : add up the very first 2 terms, pulling out choose factors:a•(a-6) add up the critical 2 terms, pulling out typical factors:3•(a-6) Step-5:Add up the four terms of step4:(a-3)•(a-6)Which is the wanted factorization

Canceling out :

2.3 Cancel out (a-3) which shows up on both political parties of the portion line.

See more: What Are The Prime Numbers Of 63 ? What Is The Prime Factorization Of 63

Equation at the end of step 2 :

(a + 1) (a - 6) ——————— - ——————— a - 6 a + 8

## Step 3 :

Calculating the Least common Multiple :3.1 find the Least typical Multiple The left denominator is : a-6 The best denominator is : a+8

Number of times every Algebraic Factorappears in the administrate of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
a-6101
a+8011

Least common Multiple: (a-6)•(a+8)

Calculating multiplier :

3.2 calculation multipliers for the 2 fractions represent the Least typical Multiple through L.C.M represent the Left Multiplier through Left_M signify the appropriate Multiplier through Right_M signify the Left Deniminator by L_Deno denote the right Multiplier by R_DenoLeft_M=L.C.M/L_Deno=a+8Right_M=L.C.M/R_Deno=a-6

Making identical Fractions :

3.3 Rewrite the 2 fractions into identical fractionsTwo fountain are dubbed equivalent if they have the very same numeric value. For example : 1/2 and also 2/4 space equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are tantamount as well. To calculate equivalent fraction , main point the numerator of every fraction, through its respective Multiplier.

L. Mult. • L. Num. (a+1) • (a+8) —————————————————— = ————————————— L.C.M (a-6) • (a+8) R. Mult. • R. Num. (a-6) • (a-6) —————————————————— = ————————————— L.C.M (a-6) • (a+8)Adding fountain that have a typical denominator :3.4 including up the two identical fractions include the two identical fractions i beg your pardon now have a common denominatorCombine the numerators together, put the sum or distinction over the common denominator then reduce to lowest terms if possible:

(a+1) • (a+8) - ((a-6) • (a-6)) 21a - 28 ——————————————————————————————— = ————————————————— (a-6) • (a+8) (a - 6) • (a + 8)

## Step 4 :

Pulling out choose terms :4.1 traction out prefer factors:21a - 28=7•(3a - 4)