Question

solve the linear equation of x+4/x-4 - x-4/x+4=1-x^2/x^2-16 ​

Answer 1

Step-by-step explanation:

x+4 - x-4 = 1-x^2

x-4 x+4 x^2-16

(x+4)2 - (x-4)2= 1-x^2

( x-4) (x+4) x^2-16

(x2+16+8x)-(x2+16-8x) = 1-x^2

( x-4) (x+4) x^2-16

x2+16+8x-x2-16+8x =1-x^2

( x-4) (x+4) x^2-16

ab solve ho jana cahiye right.so solve it your self.

Answer 2

$\large\underline{\text{Note}}$

The given equation is referred to as a rational equation. Extraneous solutions are solutions that appear when solving the equation but don't actually satisfy the equation. (may appear in equations involving surds or fractions)

$\large\underline{\text{Solution}}$

Given equation is,

$\implies\dfrac{x+4}{x-4}-\dfrac{x-4}{x+4}=1-\dfrac{x^{2}}{x^{2}-16}$

To eliminate the denominator, multiply $(x^{2}-16)$.

$\implies(x+4)^{2}-(x-4)^{2}=(x^{2}-16)-x^{2}$

$\implies(x^{2}+8x+16)-(x^{2}-8x+16)=(x^{2}-16)-x^{2}$

$\implies 16x=-16$

$\implies x=-1$

This is a solution as it doesn't belong to the value that makes the denominator equals to zero.

$\large\underline{\text{Conclusion}}$

$x=-1$ is the solution of the rational equation.