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4vir4ik [10]
3 years ago
13

What is the solution to the equation x+3/x+2=3+1/x

Mathematics
2 answers:
victus00 [196]3 years ago
8 0

Answer:

x=-1

Step-by-step explanation:

x+3

------- = 3 + 1/x

x+2

Get a common denominator on the right

3*x/x + 1/x

3x/x + 1/x = (3x+1)/x


x+3       3x+1

------- = ---------

x+2         x


We can use cross products to solve

(x+3) *x = (3x+1) * (x+2)

x^2+3x = 3x*x +x + 3x*2 +2

Simplifying

x^2 + 3x = 3x^2 +7x+2

Subtract x^2 from each side

x^2 -x^2 + 3x = 3x^2-x^2 +7x+2

3x = 2x^2 +7x+2

Subtract 3x from each side

3x-3x = 2x^2 +7x -3x+2

0 = 2x^2 +4x +2

Divide by 2

0 = x^2 +2x +1

Factor

0 = (x+1) (x+1)

Using the zero product property

x+1 =0

x=-1

marishachu [46]3 years ago
6 0

Answer:

The solution set is { -1 }.

Step-by-step explanation:

If we multiply each term by the LCM of x and x+ 2 ( = x(x + 2))  we get:-

x(x + 3) = 3x(x + 2)  + x + 2

x^2 + 3x = 3x^2 + 6x + x + 2

0 = 3x^2 - x^2 - 3x + 6x + x + 2

2x^2 +4x + 2 = 0

2(x^2 + 2x + 1) = 0

2( x + 1)(x + 1) = 0

x = -1    Multiplicity 2

The solution set  only contains 1 * -1 . Elements in a set are not repeated

So   its {-1}  (answer)


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Help help help help help
liubo4ka [24]

Answer:

m(∠y) = 64°

Step-by-step explanation:

From the figure attached,

m(∠e) = 90°

m(∠b) + 67° = 180° [Linear pair of angles]

m(∠b) = 180 - 67

          = 113°

m(∠c) + 75° = 180°  [Linear pair of angles]

m(∠c) = 105°

m(∠a) = m(∠d)

By the property of a polygon,

Sum of the interior angles of a polygon is given by,

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Here, n = number of sides of the polygon

For n = 5,

Sum of interior angles = (5 - 2)×180°

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m(∠a) + m(∠b) + m(∠c) + m(∠d) + m(e) = 540°

2m(∠d) + 113° + 105° + 90° = 540°

2m(∠d) + 308 = 540°

2m(∠d) = 540 - 308

m(∠d) = 116°

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m(∠y) + 116° = 180° [Linear pair of angles]

m(∠y) = 64°

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