$\displaystyle\\\\\frac{2}{x-2}+\frac{7}{x^2-4}=\frac{5}{x}\\\\\frac{^{x+2)}2~~~~~}{x-2}+\frac{7}{(x-2)(x+2)}=\frac{5}{x}\\\\\frac{2(x+2)}{(x-2)(x+2)}+\frac{7}{(x-2)(x+2)}=\frac{5}{x}\\\\\frac{2x+4+7}{x^2-4}=\frac{5}{x}\\\\\frac{2x+11}{x^2-4}=\frac{5}{x}\\\\5(x^2-4)=x(2x+11)\\\\5x^2-20=2x^2+11x\\\\5x^2-2x^2 -11x-20=0$

$\displaystyle\\3x^2-11x-20=0\\\\x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{11\pm\sqrt{121+4\cdot3\cdot20}}{2\cdot3}=\\\\=\frac{11\pm\sqrt{121+240}}{6}=\frac{11\pm\sqrt{361 }}{6}=\frac{11\pm19}{6}\\\\x_1=\frac{11-19}{6}=\frac{-8}{6}\\\\\boxed{\bf x_1=-\frac{4}{3}}\\\\x_2=\frac{11+19}{6}=\frac{30}{6}\\\\\boxed{\bf x_2=5}$

3 0

3 years ago

What postulate or theorem can be used to prove that these two triangles are congruent?

Diano4ka-milaya [45]

Answer:

ASA

Step-by-step explanation:

in the place that I have put some marks on it, they have the same angle; so then they will also have the same third angle; and for the rest you should use ASA.

8 0

3 years ago

Determine the answer to 3 + (-5) and explain the steps using a number line

Andreas93 [3]

Answer:

-2

Step-by-step explanation:

3 - 5 = -2

Place the dot on -2 on the number line that is on your problem as the answer. To show the steps on the number line, use your jumps to go back. For example, your starting point will be on 3, and then use your jumps to go back by 5; that means you go into the negatives. For this case, it is -2.

4 0

3 years ago