Question

Prosze o pilne rozwiazanie tego zadania

Answer 1

a)

7/(x +1) = 3/(x +5);  dla  x ≠ -1   i   x ≠ -5

7(x + 5) = 3(x +1)

7x + 35 = 3x +3

7x - 3x = 3 - 35

4x = - 32

x = -8

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b)

(x - 49)/(x²² - 7x) = 8/(x -7) ;  dla   x ≠ 7

(x - 49)(x -7) = 8(x² - 7x)

x²-7x - 49x + 343 = 8x² - 56x

7 x² - 343 = 0 / : 7

x² - 49 = 0

(x + 7)(x - 7) = 0

x = - 7  lub x = 7 , ale x ≠ 7

zatem Odp.x = -7

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c)

[4x -2]/[3 - 2x] = 1/2; dla  x ≠ 1,5

2 [4x - 2] = 3 - 2x

8x -4 = 3 - 2x

8x +2x = 3 + 4

10x = 7

x = 0,7

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d)

x/[x -1] = [x =2]/x  ;  dla  x ≠ 0  i x ≠ 1

x² = x² +2x - x -2

0 = x - 2

x = 2

==========

e)

5/x = 4;  dla x ≠ 0

5 = 4x

x = 5/4 = 1,25

=================

f)

[5x +4]/[2x -1] = 3;  dla x ≠ 1/2

5x + 4 = 3(2x -1)

5x + 4 = 6x - 3

6x -5x = 4 + 3

x = 7

=================

g) [6x - 4]/[2 - 3x] = -2 ;  dla x ≠ 2/3

6x - 4 = -2[2 - 3x]

6x - 4 = -4 +6x

0 = 0

x ∈ R

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h)

[x+1]/[2x -1] - 2/x = 0 ; dla  x ≠ 1/2

[x +1]/[2x -1] = 2/x

2(2x -1) = x (x +1)

4x - 2 = x² + x

x² -3x + 2 = 0

(x -2)(x -1) = 0

x = 2  lub x = 1

=================

i)

2/[x +2] - 1/[x - 3] = 0;  dla x ≠ -2  i x≠ 3

2/[x + 2] = 1/[x -3]

2 [x -3] = x + 2

2x - 6 = x + 2

2x - x = 2 + 6

x = 8

=========

j)

[1 - 2x]/[x +1] = 8;  dla x ≠ -1

1 - 2x = 8[x + 1]

1 - 2x = 8x + 8

8x + 2x = 1 - 8

10x = - 7

x =  - 0,7

============

k)

[4x -2]/[3 - 2x] = -1/2;  dla x ≠ 3/2

4x -2 = -0,5 [3 - 2x]

4x - 2 = -1,5 + x

4x -x = -1,5 + 2

3x = 0,5 = 1/2

x =(1/2 ) : 3

x = 1/6

=================

l)

[7x + 6]/[1 - 3x] = -4 ;  dla   x ≠ 1/3

7x + 6 = -4[1 - 3x]

7x + 6 = -4 +12x

12x - 7x = 6 + 4

5x = 10 / : 5

x = 2

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