Solve 154/1+x-90/1-x=40sqrt{45}x^25292656(xdiv2^22^22x525051sqrt{9}

$$\frac{ 154 }{ 1+x } - \frac{ 90 }{ 1-x } = 40 \sqrt{ 45 } { x }^{ 2 } 5292656(x \div { 2 }^{ 2 } { 2 }^{ 2 } 2x525051 \sqrt{ 9 }$$

Solve for x_525051

$$x_{525051}=-\frac{\sqrt{5}\left(16-61x\right)}{4763390400\left(x^{2}-1\right)x^{3}}$$

$$x\neq 0\text{ and }|x|\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of 1+x,1-x.

$$\left(x-1\right)\times 154-\left(-\left(1+x\right)\times 90\right)=40\times 5292656\sqrt{45}x^{2}\times 2\left(x\div 2^{2}\right)\times 2^{2}x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(x-1\right)\times 154-\left(-\left(1+x\right)\times 90\right)=40\times 5292656\sqrt{45}x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply x-1 by 154.

$$154x-154-\left(-\left(1+x\right)\times 90\right)=40\times 5292656\sqrt{45}x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

Multiply -1 and 90 to get -90.

$$154x-154-\left(-90\left(1+x\right)\right)=40\times 5292656\sqrt{45}x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply -90 by 1+x.

$$154x-154-\left(-90-90x\right)=40\times 5292656\sqrt{45}x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

To find the opposite of -90-90x, find the opposite of each term.

$$154x-154+90+90x=40\times 5292656\sqrt{45}x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

Add -154 and 90 to get -64.

$$154x-64+90x=40\times 5292656\sqrt{45}x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

Combine 154x and 90x to get 244x.

$$244x-64=40\times 5292656\sqrt{45}x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

Factor 45=9\times 5. Rewrite the square root of the product \sqrt{9\times 5} as the product of square roots \sqrt{9}\sqrt{5}.

$$244x-64=40\times 5292656\sqrt{9}\sqrt{5}x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{9}\left(x-1\right)\left(x+1\right)$$

Multiply \sqrt{9} and \sqrt{9} to get 9.

$$244x-64=40\times 5292656\times 9x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{5}\left(x-1\right)\left(x+1\right)$$

Multiply 40 and 5292656 to get 211706240.

$$244x-64=211706240\times 9x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{5}\left(x-1\right)\left(x+1\right)$$

Multiply 211706240 and 9 to get 1905356160.

$$244x-64=1905356160x^{2}\times 2^{3}\left(x\div 2^{2}\right)x_{525051}\sqrt{5}\left(x-1\right)\left(x+1\right)$$

Calculate 2 to the power of 3 and get 8.

$$244x-64=1905356160x^{2}\times 8\left(x\div 2^{2}\right)x_{525051}\sqrt{5}\left(x-1\right)\left(x+1\right)$$

Multiply 1905356160 and 8 to get 15242849280.

$$244x-64=15242849280x^{2}\left(x\div 2^{2}\right)x_{525051}\sqrt{5}\left(x-1\right)\left(x+1\right)$$

Calculate 2 to the power of 2 and get 4.

$$244x-64=15242849280x^{2}\left(x\div 4\right)x_{525051}\sqrt{5}\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply 15242849280x^{2}\left(x\div 4\right)x_{525051}\sqrt{5} by x-1.

$$244x-64=\left(15242849280\left(x\div 4\right)x_{525051}\sqrt{5}x^{3}-15242849280x_{525051}x^{2}\left(x\div 4\right)\sqrt{5}\right)\left(x+1\right)$$

Use the distributive property to multiply 15242849280\left(x\div 4\right)x_{525051}\sqrt{5}x^{3}-15242849280x_{525051}x^{2}\left(x\div 4\right)\sqrt{5} by x+1 and combine like terms.

$$244x-64=15242849280\left(x\div 4\right)x_{525051}\sqrt{5}x^{4}-15242849280x_{525051}x^{2}\left(x\div 4\right)\sqrt{5}$$

Swap sides so that all variable terms are on the left hand side.

$$15242849280\left(x\div 4\right)x_{525051}\sqrt{5}x^{4}-15242849280x_{525051}x^{2}\left(x\div 4\right)\sqrt{5}=244x-64$$

Combine all terms containing x_{525051}.

$$\left(15242849280\left(x\div 4\right)\sqrt{5}x^{4}-15242849280x^{2}\left(x\div 4\right)\sqrt{5}\right)x_{525051}=244x-64$$

The equation is in standard form.

$$\left(3810712320\sqrt{5}x^{5}-3810712320\sqrt{5}x^{3}\right)x_{525051}=244x-64$$

Divide both sides by 3810712320x^{5}\sqrt{5}-3810712320x^{3}\sqrt{5}.

$$\frac{\left(3810712320\sqrt{5}x^{5}-3810712320\sqrt{5}x^{3}\right)x_{525051}}{3810712320\sqrt{5}x^{5}-3810712320\sqrt{5}x^{3}}=\frac{244x-64}{3810712320\sqrt{5}x^{5}-3810712320\sqrt{5}x^{3}}$$

Dividing by 3810712320x^{5}\sqrt{5}-3810712320x^{3}\sqrt{5} undoes the multiplication by 3810712320x^{5}\sqrt{5}-3810712320x^{3}\sqrt{5}.

$$x_{525051}=\frac{244x-64}{3810712320\sqrt{5}x^{5}-3810712320\sqrt{5}x^{3}}$$

Divide 244x-64 by 3810712320x^{5}\sqrt{5}-3810712320x^{3}\sqrt{5}.

$$x_{525051}=\frac{\sqrt{5}\left(61x-16\right)}{4763390400\left(x^{2}-1\right)x^{3}}$$