### 3/(4x+3)+21/(8x^2-14x-15)

This faces adding, subtracting and also finding the least common multiple.

You are watching: What is the simplified form of 3 over 4x plus 3 + 21 over 8 x squared minus 14x minus 15 ?

## Step by action Solution ## Step 1 :

Equation in ~ the finish of step 1 : 3 21 ———————— + ——————————————————— (4x + 3) ((23x2 - 14x) - 15)

## Step 2 :

21 simplify —————————————— 8x2 - 14x - 15Trying to factor by dividing the middle term2.1Factoring 8x2 - 14x - 15 The very first term is, 8x2 that is coefficient is 8.The center term is, -14x that coefficient is -14.The last term, "the constant", is -15Step-1 : multiply the coefficient that the an initial term through the consistent 8•-15=-120Step-2 : find two factors of -120 who sum equates to the coefficient the the middle term, i beg your pardon is -14.

 -120 + 1 = -119 -60 + 2 = -58 -40 + 3 = -37 -30 + 4 = -26 -24 + 5 = -19 -20 + 6 = -14 That"s it

Step-3 : Rewrite the polynomial separating the center term using the two factors found in step2above, -20 and also 68x2 - 20x+6x - 15Step-4 : include up the first 2 terms, pulling out choose factors:4x•(2x-5) include up the last 2 terms, pulling out common factors:3•(2x-5) Step-5:Add increase the 4 terms of step4:(4x+3)•(2x-5)Which is the preferred factorization

Equation at the finish of step 2 :

3 21 ———————— + ——————————————————— (4x + 3) (2x - 5) • (4x + 3)

## Step 3 :

3 simplify —————— 4x + 3Equation at the finish of step 3 : 3 21 —————— + ——————————————————— 4x + 3 (2x - 5) • (4x + 3)

## Step 4 :

Calculating the Least common Multiple :4.1 uncover the Least typical Multiple The left denominator is : 4x+3 The right denominator is : (2x-5)•(4x+3)

Number the times each Algebraic Factorappears in the administer of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
4x+3111
2x-5011

Least usual Multiple: (4x+3)•(2x-5)

Calculating multipliers :

4.2 calculate multipliers for the two fractions denote the Least typical Multiple by L.C.M signify the Left Multiplier through Left_M denote the appropriate Multiplier by Right_M represent the Left Deniminator by L_Deno represent the appropriate Multiplier by R_DenoLeft_M=L.C.M/L_Deno=2x-5Right_M=L.C.M/R_Deno=1

Making tantamount Fractions :

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

L. Mult. • L. Num. 3 • (2x-5) —————————————————— = ——————————————— L.C.M (4x+3) • (2x-5) R. Mult. • R.

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Num. 21 —————————————————— = ——————————————— L.C.M (4x+3) • (2x-5)Adding fountain that have a usual denominator :4.4 including up the two indistinguishable fractions add the two tantamount fractions which now have a common denominatorCombine the numerators together, put the amount or difference over the usual denominator then reduce to lowest state if possible:

3 • (2x-5) + 21 6x + 6 ——————————————— = ——————————————————— (4x+3) • (2x-5) (4x + 3) • (2x - 5)

## Step 5 :

Pulling out like terms :5.1 pull out prefer factors:6x + 6=6•(x + 1)