Rational equations and inequalities

1003136402

Level: 
A
Choose the operation, which most effectively eliminates fractions from the equation. \[ \frac2{x^2-9}+\frac3{3-x}=\frac{x+1}{2x} \]
multiplying both sides by \( 2x\left(x^2-9\right) \)
multiplying both sides by \( 2x\left(x^2-9\right)(3-x) \)
multiplying both sides by \( 2x^2-9 \)
multiplying both sides by \( 18x^2 \)

1003136401

Level: 
A
Choose the operation, which most effectively eliminates fractions from the equation. \[ 3+\frac2{x+4}=\frac1{3x+12} \]
multiplying both sides by \( 3x+12 \)
multiplying both sides by \( (x+4)(3x+12) \)
subtracting \( \frac2{x+4} \) from both sides
multiplying both sides by \( 12x \)

1003138305

Level: 
B
Choose the resulting form of the given inequality after multiplying both sides by \( (x-1)(x-2) \), where \( x\in(0;1) \). \[ 1 \leq \frac{x-3}{1-x}+\frac{x-1}{x-2} \]
\( (x-1)(x-2) \leq (3-x)(x-2)+(x-1)(x-1) \)
\( (x-1)(x-2) \geq (x-3)(2-x)+(x-1)(x-1) \)
\( (x-1)(x-2) \leq (x-3)(x-2)+(x-1)(x-1) \)
\( (x-1)(x-2) \leq -x-3(x-2)+(x-1)^2 \)

1003138302

Level: 
B
Choose the resulting form of the given inequality after multiplying both sides by \( x^2-25 \), where \( x\in(-1;1) \). \[ \frac{3+x}{x+5}-\frac{x+1}{x-5} < \frac x{x^2-25} \]
\( (3+x)(x-5)-(x+1)(x+5) > x \)
\( (3+x)(x-5)-(x+1)(x+5) < x \)
\( (3+x)(x-5)+(x+1)(x+5) > x \)
\( (3+x)(x+5)-(x+1)(x-5) > x \)

1003138301

Level: 
B
Choose the resulting form of the given inequality after multiplying both sides by \( x^2-16 \), where \( x\in(4;\infty) \). \[ \frac1{x^2-16}-\frac x{4-x} < \frac{3+x}{x+4} \]
\( 1+x(x+4) < (3+x)(x-4) \)
\( 1-x(x+4) < (3+x)(x-4) \)
\( 1+x(x+4) > (3+x)(x-4) \)
\( 1-x(x-4) > (3+x)(x+4) \)