x²-16/x+4 ÷x-4/x+4 =
Answers
Rewrite 16 as 42
.
x2−42x−4=x+4
Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)
where a=x and b=4
.
(x+4)(x−4)x−4=x+4
Reduce the expression by cancelling the common factors.
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Reduce the expression (x+4)(x−4)x−4
by cancelling the common factors.
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Cancel the common factor.
(x+4)(x−4
)x−4=x+4
Rewrite the expression.
x+41=x+4
Divide x+4
by 1
.
x+4=x+4
Move all terms containing x
to the left side of the equation.
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Subtract x
from both sides of the equation.
x+4−x=4
Combine the opposite terms in x+4−x
.
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Subtract x
from x
.
0+4=4
Add 0
and 4
.
4=4
Since 4=4
, the equation will always be true for any value of x
.
All real numbers
The result can be shown in multiple forms.
All real numbers
Interval Notation:
(−∞,∞)
The answer is x+4
Given:
x²-16/x+4 ÷x-4/x+4 =
To find:
The value of x²-16/x+4 ÷x-4/x+4
Solution:
Given x²-16/x+4 ÷x-4/x+4
=
= [ x+4 will be cancelled ]
=
As we know a²-b² = (a+b)(a-b)
=
= x+4 [ (x-4) will be cancelled ]
The value of x²-16/x+4 ÷x-4/x+4 = x+4
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