Question

solve 2/(x - 3) + 1/(x - 1) = 5/(x - 1) - 2/(x - 2)

Answer 1

Step-by-step explanation:

One solution was found :

x = 7/3 = 2.333

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2/(x-3)+1/(x-1)-(5/(x-1)-2/(x-2))=0

Step by step solution :

Step 1 :

2

Simplify —————

x - 2

Equation at the end of step 1 :

2 1 5 2

(—————+—————)-(—————-———) = 0

(x-3) (x-1) (x-1) x-2

Step 2 :

5

Simplify —————

x - 1

Equation at the end of step 2 :

2 1 5 2

(—————+—————)-(———-———) = 0

(x-3) (x-1) x-1 x-2

Step 3 :

Calculating the Least Common Multiple :

3.1 Find the Least Common Multiple

The left denominator is : x-1

The right denominator is : x-2

Number of times each Algebraic Factor

appears in the factorization of:

Algebraic

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

x-1 1 0 1

x-2 0 1 1

Least Common Multiple:

(x-1) • (x-2)

Calculating Multipliers :

3.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = x-2

Right_M = L.C.M / R_Deno = x-1