Chapter 7: Q. 36 (page 652)

Multiply the rational expressions $\frac{z^{2} + 3 z}{z^{2} - 3 z - 4} \times \frac{z - 4}{z^{2}}$

Short Answer

Expert verified

Simplified form of the multiplied rational expressions $\frac{z^{2} + 3 z}{z^{2} - 3 z - 4} \times \frac{z - 4}{z^{2}} i s \frac{z + 3}{z (z + 1)}, z \neq - 1$

Step by step solution

. Given information

Given expressions are $\frac{z^{2} + 3 z}{z^{2} - 3 z - 4} a r e \frac{z - 4}{z^{2}} .$

We have to multiply the given rational expressions.

. Explanation of multiplying rational fractions

To multiply the given rational fraction , we need to factor numerator and denominator separately. After that multiply the numerators and denominators and divide out the common factors , then simplify the expressions.

. Multiplication of rational expressions

Here when we do the multiplication of the given rational expressions become, $\frac{z^{2} + 3 z}{z^{2} - 3 z - 4} \times \frac{z - 4}{z^{2}} = \frac{z (z + 3)}{(z - 4) (z + 1)} \times \frac{z - 4}{z^{2}}, f a c t o r t h e n u m e r a t o r a n d d e n o m i n a t o r = \frac{z (z + 3) \times (z - 4)}{(z - 4) (z + 1) \times z^{2}}, m u l t i p l y t h e n u m e r a t o r s a n d d e n o m i n a t o r s = \frac{(z + 3)}{z (z + 1)} d i v i d e o u t t h e c o m m o n f a c t o r s a n d s i m p l i f y = \frac{(z + 3)}{z (z + 1)}, z \neq - 1 t h i s i s t h e s i m p l i f i e d f o r m .$

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Multiply the rational expressions $\frac{z^{2} + 3 z}{z^{2} - 3 z - 4} \times \frac{z - 4}{z^{2}}$

Short Answer

Step by step solution

. Given information

. Explanation of multiplying rational fractions

. Multiplication of rational expressions

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Multiply the rational expressionsz2+3zz2-3z-4×z-4z2

Short Answer

Step by step solution

. Given information

. Explanation of multiplying rational fractions

. Multiplication of rational expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

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Logic and Functions

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Multiply the rational expressions $\frac{z^{2} + 3 z}{z^{2} - 3 z - 4} \times \frac{z - 4}{z^{2}}$