Simplify x² - 9 / х^2 - 3x
2 answers:
Answer:
Step-by-step explanation:
Factorise numerator and denominator
x² - 9 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
x² - 9
= x² - 3² = (x - 3)(x + 3)
x² - 3x ← factor out x from each term
= x(x - 3)
Then
= ← cancel common factor (x - 3) on numerator/denominator
=
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As is shown in the figure attached:
1. "A" and 76º are congruents, because they are Alternate Interior angles, so A=76º.
2. "D" and "x" are congruents, because they are Alternate Interior angles, so x=38º.
3. "A", "B" and "C" form a the triangle ABC. Then, we remember sum of the interior angles of a triangle is 180º, so we have:
76º+38º+B=180º
B=180º-76º-38º
B=66º
4. By definition, an exterior angle of a triangle is equal to the sum of the opposite interior angles to it. So, we can calculate the exterior angle "y" of the triangle ABC, as follows:
The opposite angles are: 76º and 66ª. Then, we obtain:
y=76º+66º
y=142º
Therefore, the answer is: The value of y is 142º.
1. "A" and 76º are congruents, because they are Alternate Interior angles, so A=76º.
2. "D" and "x" are congruents, because they are Alternate Interior angles, so x=38º.
3. "A", "B" and "C" form a the triangle ABC. Then, we remember sum of the interior angles of a triangle is 180º, so we have:
76º+38º+B=180º
B=180º-76º-38º
B=66º
4. By definition, an exterior angle of a triangle is equal to the sum of the opposite interior angles to it. So, we can calculate the exterior angle "y" of the triangle ABC, as follows:
The opposite angles are: 76º and 66ª. Then, we obtain:
y=76º+66º
y=142º
Therefore, the answer is: The value of y is 142º.