### ((r+5)/(r2+5r-14))/((r2+4r-21)/(r-2))

This encounters simplification or other basic results.

You are watching: Divide r+5/r^2+5r-14 by r^2+4r-21/r-2

## Step by step Solution ### Reformatting the intake :

Changes do to your input should not affect the solution: (1): "r2" was changed by "r^2". 1 much more similar replacement(s).

## Step 1 :

r2 + 4r - 21 simplify ———————————— r - 2 do the efforts to variable by dividing the middle term1.1Factoring r2 + 4r - 21 The an initial term is, r2 the coefficient is 1.The middle term is, +4r that is coefficient is 4.The critical term, "the constant", is -21Step-1 : multiply the coefficient that the very first term by the continuous 1•-21=-21Step-2 : discover two determinants of -21 who sum equates to the coefficient that the center term, which is 4.

 -21 + 1 = -20 -7 + 3 = -4 -3 + 7 = 4 That"s it

Step-3 : Rewrite the polynomial dividing the middle term making use of the two factors found in step2above, -3 and also 7r2 - 3r+7r - 21Step-4 : include up the first 2 terms, pulling out like factors:r•(r-3) include up the last 2 terms, pulling out typical factors:7•(r-3) Step-5:Add up the four terms of step4:(r+7)•(r-3)Which is the preferred factorization

Equation in ~ the finish of step 1 :

(r+5) (r+7)•(r-3) —————————————— ÷ ——————————— (((r2)+5r)-14) r-2

## Step 2 :

r + 5 simplify ———————————— r2 + 5r - 14Trying to element by dividing the center term2.1Factoring r2 + 5r - 14 The an initial term is, r2 the coefficient is 1.The center term is, +5r its coefficient is 5.The last term, "the constant", is -14Step-1 : multiply the coefficient of the an initial term by the continuous 1•-14=-14Step-2 : uncover two determinants of -14 whose sum amounts to the coefficient the the middle term, i beg your pardon is 5.

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 -14 + 1 = -13 -7 + 2 = -5 -2 + 7 = 5 That"s it

Step-3 : Rewrite the polynomial dividing the center term using the two factors found in step2above, -2 and also 7r2 - 2r+7r - 14Step-4 : add up the very first 2 terms, pulling out prefer factors:r•(r-2) include up the last 2 terms, pulling out common factors:7•(r-2) Step-5:Add up the 4 terms of step4:(r+7)•(r-2)Which is the preferred factorization

Equation at the end of action 2 :

(r + 5) (r + 7) • (r - 3) ————————————————— ÷ ————————————————— (r + 7) • (r - 2) r - 2

## Step 3 :

r+5 (r+7)•(r-3) division ——————————— by ——————————— (r+7)•(r-2) (r-2) 3.1 dividing fractions To division fractions, create the divison together multiplication by the mutual of the divisor :

r + 5 (r + 7) • (r - 3) r + 5 r - 2 ————————————————— ÷ ————————————————— = ————————————————— • —————————————————(r + 7) • (r - 2) (r - 2) (r + 7) • (r - 2) (r + 7) • (r - 3)Canceling the end :3.2 Cancel out (r - 2) which shows up on both political parties of the portion line.

Multiplying Exponential Expressions:

3.3 main point (r + 7) by (r + 7)The ascendancy says : To main point exponential expression which have the very same base, add up their exponents.In our case, the common base is (r+7) and the exponents are:1,as(r+7) is the same number together (r+7)1and1,as(r+7) is the same number together (r+7)1The product is therefore, (r+7)(1+1) = (r+7)2