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Nina [5.8K]
3 years ago
13

Simplify the rational expression x^2-4/x^2+5x+6. State any restrictions on the variable.

Mathematics
1 answer:
lianna [129]3 years ago
7 0

Answer:

The correct answer is option B.

Step-by-step explanation:

The given rational expression is:

\frac{x^2-4}{x^2+5x+6}

Factor the numerator and the denominator:

\frac{x^2-2^2}{x^2+2x+3x+6}

Factor the numerator using difference of two squares and the denominator using factorization by grouping.

\frac{(x-2)}{x(x+2)+3(x+2)}

\frac{(x-2)(x+2)}{(x+2)(x+3)}

This function is defined if and only if the denominator is not zero.

That is: (x+3)(x+2)≠0.

x≠-2,x≠-3

We simplify now to obtain:

\frac{x-2}{x+3}

The correct choice is the second option.

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Y = 3x

Proof:

3(1) = 3

3(3) = 9


5. 9(3) = 27

6. 27(3) = 81

7. 81(3) = 243


The 7th term is 243.
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Solve the simultaneous equations x2 + y2 = 10 and x – 3y + 10 = 0.
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x = - 1, y = 3  or     (-1 , 3)

Step-by-step explanation:

x – 3y + 10 = 0              x = 3y - 10    ... plug in

x² + y² = 10

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3 years ago
Find the quotient 1/5 divided by 2
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Answer:

Step-by-step explanation:

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Is the line y=5 parallel or perpendicular to the x- axis? Explain your answer.
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6 0
3 years ago
larry and time were standing next to each other in the backyard when Tom challenged Larry to guess how tall he is. Larry knee hi
MrRissso [65]

Answer:

6.3 feet

Step-by-step explanation:

Let the height of Tom be x feet.

Let h_{L} be height of Larry,  s_{L} be shadow height of Larry and  s_{T} be shadow height of Tom.

As per question,

h_{L}=6.5\textrm{ ft}\\s_{L}=8\textrm{ ft}\\s_{T}=7.75\textrm{ ft}

As both Tom and Larry are standing next to each other,

So, the ratio of height of Tom to that of Larry will be equal to the ratio of shadow height of Tom to that of shadow height of Larry.

\frac{x}{h_{L}}=\frac{s_{T}}{s_{L}}

Now, plug in the values and solve for x.

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Therefore, the height of Tom is 6.3 feet.

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4 years ago
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