Question

solve for x...

2(x-1/x+3) -7(x+3/x-1) = 5

Answer 1

here's your answer

value of x can be either -23/5 or -1

Answer 2

The value of x is -23/5 or -1

Step-by-step explanation:

Consider the provided expression.

$2\left(\frac{x-1}{x+3}\right)-7\left(\frac{x+3}{x-1}\right)=5$

Multiply by least common multiple $\left(x+3\right)\left(x-1\right)$

$2\left(x-1\right)^2-7\left(x+3\right)^2=5\left(x+3\right)\left(x-1\right)$

$2\left(x^2-2x+1\right)-7\left(x^2+6x+9\right)=5\left(x^2+2x-3\right)$

$2x^2-4x+2-7x^2-42x-63=5x^2+10x-15$

$-5x^2-46x-61=5x^2+10x-15$

$-10x^2-56x-46=0$

Use the formula: $x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute $a=-10,\:b=-56,\:c=-46$ in above formula.

$x_{1,\:2}=\frac{-\left(-56\right)\pm \sqrt{\left(-56\right)^2-4\left(-10\right)\left(-46\right)}}{2\left(-10\right)}$

$x_{1,\:2}=\frac{56\pm\sqrt{1296}}{-20}$

$x_1=-\frac{56+36}{20}\ or\ x_2=-\frac{56-36}{20}\\\\x_1=-\frac{23}{5}\ or\ x_2=-1$

Hence, the value of x is -23/5 or -1

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Solve for x. x/3-5=8