Question

x²-16/x+4 ÷x-4/x+4 =​

Answer 1

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.

Tap for fewer steps...

Reduce the expression (x+4)(x−4)x−4

by cancelling the common factors.

Tap for fewer steps...

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.

Tap for fewer steps...

Subtract x

from both sides of the equation.

x+4−x=4

Combine the opposite terms in x+4−x

.

Tap for fewer steps...

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:

(−∞,∞)

Answer 2

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

=  $\frac{ x^{2} -16/x+4}{x-4/x+4}$

= $\frac{ x^{2} -16}{x-4}$     [ x+4 will be cancelled ]

= $\frac{ x^{2} -4^{2} }{x-4}$

As we know a²-b² = (a+b)(a-b)

= $\frac{ (x -4)(x+4)}{x-4}$  

= x+4     [ (x-4) will be cancelled ]

The value of x²-16/x+4 ÷x-4/x+4 = x+4

#SPJ2