Answer:
<em>If statement(1) holds true, it is correct that </em>
<em> is an integer.</em>
<em>If statement(2) holds true, it is not necessarily correct that </em>
<em> is an integer.</em>
<em></em>
Step-by-step explanation:
Given two positive integers
and
.
To check whether
is an integer:
Condition (1):
Every factor of
is also a factor of
.

Let us consider an example:

which is an integer.
Actually, in this situation
is a factor of
.
Condition 2:
Every prime factor of <em>s</em> is also a prime factor of <em>r</em>.
(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)
Let


which is not an integer.
So, the answer is:
<em>If statement(1) holds true, it is correct that </em>
<em> is an integer.</em>
<em>If statement(2) holds true, it is not necessarily correct that </em>
<em> is an integer.</em>
<em></em>
Answer:
x = - 3 and x = 1
Step-by-step explanation:
Given the rational expression

The denominator of the expression cannot be zero as this would make the expression undefined. Equating the denominator to zero and solving gives the values that x cannot be, that is
x² + 2x - 3 = 0 ← in standard form
(x + 3)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 1 = 0 ⇒ x = 1
Thus x = 1 and x = - 3 are both excluded values
Answer:
3x was subtracted from the left side, but 3x was subtracted from the right side. The Subtract Property of Equality states that you can subtract the same number from each side and the equation will remain true. But 3x and 3 are not the same number (unless x is 1).
x = -8/5
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
Step 2: Subtract 12 from both sides.
Step 3: Divide both sides by 10.
X = 4 and Y = 9. I did a complicated way of doing it so if u copy it it would look weird
Answer:
- Solution of equation ( q ) = <u>1</u><u>6</u>
Step-by-step explanation:
In this question we have given an equation that is <u>3 </u><u>(</u><u> </u><u>q </u><u>-</u><u> </u><u>7</u><u> </u><u>)</u><u> </u><u>=</u><u> </u><u>2</u><u>7</u><u> </u>and we have asked to solve this equation that means to find the value of <u> </u><u>q</u><u> </u><u>.</u>
<u>Solution : -</u>

<u>Step </u><u>1</u><u> </u><u>:</u> Solving parenthesis :

<u>Step </u><u>2</u><u> </u><u>:</u> Adding 21 on both sides :

On further calculations we get :

<u>Step </u><u>3 </u><u>:</u> Dividing by 3 from both sides :

On further calculations we get :

- <u>Therefore</u><u>,</u><u> </u><u>solution</u><u> </u><u>of </u><u>equation</u><u> </u><u>(</u><u> </u><u>q </u><u>)</u><u> </u><u>is </u><u>1</u><u>6</u><u> </u><u>.</u>
<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>
Now we are very our answer by substituting value of q in the given equation . So ,
<u>Therefore</u><u>,</u><u> </u><u>our </u><u>solution</u><u> </u><u>is </u><u>correct</u><u> </u><u>.</u>
<h2>
<u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>