What is the answer to 1/(x^2)-1/((x+1)^2)=1 ?

The answer to 1/(x^2)-1/((x+1)^2)=1 is x\approx-0.46898…,x\approx 0.88320…

Solve for x: 1/(x^2)-1/((x+1)^2)=1

The solution is x\approx-0.46898…,x\approx 0.88320…

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\frac{1}{x ^{2}} - \frac{1}{( x + 1 ) ^{2}} = 1

x \approx - 0.46898 \dots, x \approx 0.88320 \dots

Solution steps

\frac{1}{x ^{2}} - \frac{1}{( x + 1 ) ^{2}} = 1

Multiply by LCM

(x + 1)^{2} - x^{2} = x^{2} (x + 1)^{2}

Solve

(x + 1)^{2} - x^{2} = x^{2} (x + 1)^{2} : x \approx - 0.46898 \dots, x \approx 0.88320 \dots

x \approx - 0.46898 \dots, x \approx 0.88320 \dots

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 1

Combine undefined points with solutions:

x \approx - 0.46898 \dots, x \approx 0.88320 \dots

- \frac{2}{x + 1} - 1 = \frac{2 x}{x + 1}

y, x = \frac{y}{y + 1}

\frac{x + 1}{1 - 2 x} = \frac{5}{- 7}

- \frac{9}{x + 9} - 1 = \frac{5 x}{x + 9}

\frac{1}{x - 7} - 1 = - \frac{9 x}{x - 7}

What is the answer to 1/(x^2)-1/((x+1)^2)=1 ?
The answer to 1/(x^2)-1/((x+1)^2)=1 is x\approx-0.46898…,x\approx 0.88320…
Solve for x: 1/(x^2)-1/((x+1)^2)=1
The solution is x\approx-0.46898…,x\approx 0.88320…