Question

Answer the question attached.

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Answer 1

Given Equation

$\rm \to \: \dfrac{ {x}^{2} - (x + 2)(x - 2)}{(x + 3)} = \dfrac{1}{2}$

To find the value of 'x'

Now Take

$\rm \to \: \dfrac{ {x}^{2} - (x + 2)(x - 2)}{(x + 3)} = \dfrac{1}{2}$

We know that

$\rm \to \: (a - b)(a + b) = {a}^{2} + {b}^{2}$

We get

$\rm \: \to \: \dfrac{ {x}^{2} - ( {x}^{2} - 4) }{(x + 3)} = \dfrac{1}{2}$

$\rm \: \to \: \dfrac{ {x}^{2} - {x}^{2} + 4 }{(x + 3)} = \dfrac{1}{2}$

$\sf \to \: \dfrac{4}{(x + 3)} = \dfrac{1}{2}$

Now Using Cross multiplication method

$\sf \to \: 4 \times 2 = 1 \times (x + 3)$

$\rm \to \: x + 3 = 8$

$\rm \to \: x = 5$

Answer

$\rm \to \: x = 5$

Now Check our Answer

So Take

$\rm \to \: \dfrac{ {x}^{2} - (x + 2)(x - 2)}{(x + 3)} = \dfrac{1}{2}$

Put x = 5 , we get

$\rm \to \: \dfrac{(5) {}^{2} - (5 + 2)(5 - 2)}{(5 + 3)} = \dfrac{1}{2}$

$\rm \to \: \dfrac{25 - (7)(3)}{8} = \dfrac{1}{2}$

$\rm \to \: \dfrac{25 - 21}{8} = \dfrac{1}{2}$

$\rm \to \: \dfrac{4}{8} = \dfrac{1}{2}$

$\rm \to \: \dfrac{1}{2} = \dfrac{1}{2}$

Hence LHS = RHS

Answer 2

x = 5

Step-by-step explanation:

GIVEN:

• x²-(x+2)(x-2)/(x+3) = 1/2

TO DO:

• Solve the equation.

SOLUTION:

→ x²-(x+2)(x-2)/(x+3) = 1/2

We can see that (x+2)(x-2) is in the form of (a+b)(a-b). We know that:

• (a+b)(a-b) = a²-b²

Apply the identity:

→ x²-(x²-2²)/(x+3) = 1/2

→ x²-x²+4/(x+3) = 1/2

→ 4/(x+3) = 1/2

Now, let's solve this through Cross-multiplication:

→ (x+3) = 4×2

→ x+3 = 8

→ x= 8-3

→ x = 5

HENCE, X = 5

VERIFICATION:

=> x²-(x+2)(x-2)/(x+3) = 1/2

=> 5²-(5+2)(5-2)/5+3 = 1/2

=> (25-7×3)/8 = 1/2

=> (25-21)/8 = 1/2

=> 4/8 = 1/2

=> 1/2 = 1/2

LHS = RHS

HENCE VERIFIED!