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SAT Math : How to find the solution to a rational equation with LCD

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Example Questions

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Rational_5

Possible Answers:

–2

–1

Correct answer:

Explanation:

Rational_2

Rational_3

Rational_4

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Example Question #51 : Algebra

Linesmb1

Possible Answers:

b/(m²+ 1)

–b/(m + 1)

–b/(m²– 1)

bm/(m²+ 1)

–bm/(m²+ 1)

Correct answer:

b/(m²+ 1)

Explanation:

Linesmb5

Linesmb4

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Example Question #52 : Algebra

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?

$\frac{1}{m^3}-\frac{1}{k^2}=\frac{1}{p}$

Possible Answers:

$m=\frac{p^2k^3}{p+k^2}$

$m=(\frac{pk^2}{p+k^2})^{\frac{1}{3}}$

$m=p^{\frac{1}{2}}-k^{\frac{1}{3}}$

$m=(\frac{p+k^2}{2})^3$

$m=(\frac{p+k^2}{pk^2})^{\frac{1}{3}}$

Correct answer:

$m=(\frac{pk^2}{p+k^2})^{\frac{1}{3}}$

Explanation:

Pkm_7-21-13

Pkm2_7-21-13

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Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Solve for x:

$\frac{x+3}{7}=3$

Possible Answers:

x=24

x=6

x=42

x=0

x=18

Correct answer:

x=18

Explanation:

The first step is to cancel out the denominator by multiplying both sides by 7:

$7\cdot \frac{x+3}{7}=3\cdot7$

x+3=21

Subtract 3 from both sides to get by itself:

x+3-3=21-3

x=18

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Example Question #3 : How To Find The Solution To A Rational Equation With Lcd

Solve for and using elimination:

2x+3y=5

-x-2y=-8

Possible Answers:

x=-14 and y=11

x=14 and y=-11

x=8 and y=4

x=-8 and y=-4

$x=\frac{5}{2}$ and $y=\frac{5}{3}$

Correct answer:

x=-14 and y=11

Explanation:

When using elimination, you need two factors to cancel out when the two equations are added together. We can get the in the first equation to cancel out with the in the second equation by multiplying everything in the second equation by :

2x+3y=5

2(-x-2y)=2(-8)

Now our two equations look like this:

2x+3y=5

-2x-4y=-16

The can cancel with the -2x , giving us:

3y=5

-4y=-16

These equations, when summed, give us:

-y=-11

y=11

Once we know the value for , we can just plug it into one of our original equations to solve for the value of :

2x+3y=5

2x+3(11)=5

2x+33=5

2x=-28

x=-14

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Example Question #111 : Equations / Inequalities

Give the solution set of the rational equation $\frac{(x- 5)^{2}}{(x- 4) ^{2}} = 1$

Possible Answers:

$\left \{ - \frac{1}{2}, \frac{9}{2} \right \}$

$\left \{ 5\right \}$

$\left \{ - \frac{9}{2}, \frac{9}{2} \right \}$

$\left \{ \frac{9}{2} \right \}$

$\left \{ 4, 5\right \}$

Correct answer:

$\left \{ \frac{9}{2} \right \}$

Explanation:

Multiply both sides of the equation by the denominator $(x- 4) ^{2}$ :

$\frac{(x- 5)^{2}}{(x- 4) ^{2}} \cdot (x- 4) ^{2} =1 \cdot (x- 4) ^{2}$

$(x- 5)^{2} = (x- 4) ^{2}$

Rewrite both expression using the binomial square pattern:

$x^{2} - 2 \cdot x \cdot 5+ 5^{2} = x^{2} - 2 \cdot x \cdot 4+ 4^{2}$

$x^{2} -10x + 25 = x^{2} - 8x+16$

This can be rewritten as a linear equation by subtracting $x^{2}$ from both sides:

$x^{2} -10x + 25- x^{2} = x^{2} - 8x+16 - x^{2}$

-10x + 25 = - 8x+16

Solve as a linear equation:

-10x + 25+ 8x - 25 = - 8x+16 + 8x - 25

-2x = -9

$\frac{-2x}{-2 } =\frac{ -9 }{-2}$

$x= \frac{9}{2}$

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Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

Solve:

$\frac{10-x}{40}=-5$

Possible Answers:

x=21

x=210

x=-210

x=-200

x=200

Correct answer:

x=210

Explanation:

$\frac{10-x}{40}=-5$

Multiply by on each side

10-x=-200

Subtract on each side

-x=-210

Multiply by on each side

x=210

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SAT Math : How to find the solution to a rational equation with LCD

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Example Question #51 : Algebra

Example Question #52 : Algebra

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Example Question #3 : How To Find The Solution To A Rational Equation With Lcd

Example Question #111 : Equations / Inequalities

Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

All SAT Math Resources

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