46, 50, & 86 please Exercises 31-50 contain rational equations with denominators

Question

46, 50, & 86 please Exercises 31-50 contain rational equations with denominators For each equation, a. write the of the variable that make a denominator zero. Theo restrictions on the variable. b. Keeping the restri solve the equation. value or These are 5 10 32. x=3x+4 34.- 22 36. x 2x 5 13 2x 4 21 1 1 3x 4 6x 3 2x 3x 3 35. 2x 9 183 4 97x -4 r-2 x+ 1 37. 39.+5 15 11 40.7 x+4 x +4 41. x1 42.2-2 r + 1 43. 2x 2 2x-1 r+3 2x +6 x-2 45. 12 42-22)2) 2x x+ x-1 x2-1 48. 7 +5-525 49, 32 20 50. x+3x-2 2x-6

Explanation / Answer

46) 5 / ( x+2) + 3/ (x-2) = 12 / (x+2) (x-2)

lcd on left side is (x+2) (x-2)

5 ( x - 2) + 3 (x+2) = 12

5x - 10 + 3x + 6 = 12

8x = 16

x = 2

x cannot be 2 as it will make the denominator 0

hence, equation has no solution

50) 6 / (x+3) - 5 / (x-2) = -20 / (x^2 + x- 6 )

factoring right side bottom

6 / (x+3) - 5 / (x-2) = -20 / (x + 3) (x - 2)

multiplying entire equation by (x+3) (x-2)

6 (x-2) - 5 (x+3) = -20

6x - 12 - 5x - 15 = -20

x = -3

x cannot be -3 as it will make the denominator 0

hence , equation has NO SOLUTION

86 ) 2 (x-6) = 3x + 2 ( 2x - 1)

2x - 12 = 3x + 4x - 2

2x - 3x - 4x = 10

-5x = 10

x = -2

x^2 - x = (-2)^2 - (-2)

= 4 + 2

= 6

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