5.2 Rational equations

How many solutions does the equation [math]\displaystyle{\frac{2}{x+1}+\frac{3}{x-1}=\frac{6}{x^2-1}}[/math] have?

Solve the equation [math]\displaystyle{\frac{1}{2x+1}+\frac{1}{3x}=2}[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\displaystyle{\frac{3x}{x+1}=\frac{10}{x-1}}[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\displaystyle{\frac{1}{5(3x+1)}-\frac{1}{3(3x+1)}}=1[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\dfrac{1}{3x}+\dfrac{2x+1}{x}=3[/math]. If you have two or more answers, write the biggest one.

If [math]a+b\sqrt{c}[/math] is a solution to the equation [math]\dfrac{3x+1}{x^2-x-12}=\dfrac{1-2x}{x^2-5x+4}[/math] where [math]a[/math] and [math]b[/math] are rational numbers and [math]c[/math] is a prime number, what is the value of [math]c[/math]?

Solve the equation [math]\dfrac{x^2-6x+9}{x^2-4}\cdot\dfrac{x^2+3x+2}{x-3}=0[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\dfrac{3}{x^2+10x+12}=-\dfrac{1}{3}[/math]. If you have two or more answers, write the biggest one.

If [math]a+2\sqrt{b}[/math] is a solution to the equation [math]\dfrac{1}{(x-9)(x-11)}-\dfrac{1}{(x-1)(x-19)}=\dfrac{80}{(x-9)(x-19)}[/math] where [math]a[/math] and [math]b[/math] are integers, what is the value of [math]a-b[/math]? Hint: Let [math]x-10=A[/math].

If the rational equation [math]\dfrac{2}{x+1}+\dfrac{3}{x^2-k}=0[/math] has only one solution where [math]k[/math] is not an integer, what is the value of [math]k[/math]?

How many solutions does the equation [math]\displaystyle{\frac{5x+10}{x^2+3x+2}+\frac{7x-28}{x^2-x-12}=2}[/math] have?

Solve the equation [math]\displaystyle{\frac{x+2}{x^2-5x-6}=\frac{x-6}{x^2+3x+2}}[/math]. If you have two or more answers, write the smallest one.

Solve the equation [math]\displaystyle{\frac{2x}{x^2+4}=\frac{1}{x}}[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\displaystyle{\frac{x-6}{x-10}=\frac{2-x}{x^2-6x+8}}[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\dfrac{5}{x+1}-\dfrac{2}{x}=-4[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\dfrac{x}{x^2-4x+3}-\dfrac{3}{2x^2+2x-4}=-\dfrac{1}{x-1}[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\dfrac{3x^2-3}{x^3+1}=-2[/math]. If you have two or more answers, write the biggest one.

Solve the equation [math]\dfrac{2x}{4-x^2}+\dfrac{1}{x+2}=3[/math]. If you have two or more answers, write the smallest one.

How many solutions does the eqaution [math]\displaystyle{\frac{4x}{x+3}-\displaystyle{\frac{12}{x-3}}=\displaystyle{\frac{4x^2+36}{x^2-9}}}[/math] have?

Solve [math]\displaystyle{\frac{x+4}{x-6}+\displaystyle{\frac{x}{2}}=\displaystyle{\frac{-10}{6-x}}}[/math]. If you have two or more answers, write the biggest one.