Question

1/x-1/x+4=4/21 solve​

Answer 1

Answer:

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Step-by-step explanation:

1 Remove parentheses.

\frac{1}{x}-\frac{1}{x+4}=\frac{4}{21}

x

1

−

x+4

1

=

21

4

2 Multiply both sides by the Least Common Denominator: 21x(x+4)21x(x+4).

21(x+4)-21x=4x(x+4)21(x+4)−21x=4x(x+4)

3 Simplify.

84=4{x}^{2}+16x84=4x

2

+16x

4 Move all terms to one side.

84-4{x}^{2}-16x=084−4x

2

−16x=0

5 Factor out the common term 44.

4(21-{x}^{2}-4x)=04(21−x

2

−4x)=0

6 Factor out the negative sign.

4\times -({x}^{2}+4x-21)=04×−(x

2

+4x−21)=0

7 Divide both sides by 44.

-{x}^{2}-4x+21=0−x

2

−4x+21=0

8 Multiply both sides by -1−1.

{x}^{2}+4x-21=0x

2

+4x−21=0

9 Factor {x}^{2}+4x-21x

2

+4x−21.

(x-3)(x+7)=0(x−3)(x+7)=0

10 Solve for xx.

x=3,-7x=3,−7

Answer 2

we get the equation:

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x [x + 7] - 3 [x + 7] = 0

[x - 3] [x + 7] = 0

x = +3 or x = -7

x = -7 rejected

because negative sign can't exist.

so, x = +3.

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