How do you multiply rational equations?

How do you multiply rational equations?

To multiply rational expressions:
Completely factor all numerators and denominators. Reduce all common factors. Either multiply the denominators and numerators or leave the answer in factored form.

How do you solve rational equations?

Solution: Step 1: Factor all denominators and determine the LCD. Step 2: Identify the restrictions. In this case, they are x??2 x ? ? 2 and x??3 x ? ? 3 . Step 3: Multiply both sides of the equation by the LCD. Step 4: Solve the resulting equation. Step 5: Check for extraneous solutions.

How do you multiply and simplify rational functions?

Q and S do not equal 0.
Step 1: Factor both the numerator and the denominator. Step 2: Write as one fraction. Step 3: Simplify the rational expression. Step 4: Multiply any remaining factors in the numerator and/or denominator. Step 1: Factor both the numerator and the denominator. Step 2: Write as one fraction.

How do you multiply and divide rational expressions step by step?

How do you divide rational functions?

Step 1: Completely factor both the numerators and denominators of all fractions. Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. Step 3 : Cancel or reduce the fractions.

How to do the multiplication of rational functions?

Multiply rational functions by following the usual procedure for multiplying any fraction: 1 Step 1) Multiply the numerator by the other numerator using FOIL Method. 2 Step 2) Multiply the denominator by the other denominator using FOIL Method. 3 Step 3) Reduce/simplify the fraction (if needed) More ?

What are the steps in multiplying rational expressions?

Steps in Multiplying Rational Expressions. Multiply the numerators together Multiply the denominators together Simplify the ?new? fraction by canceling common factors when possible Let us proceed by going over five (5) worked examples in this lesson.

How to multiply rational expressions by canceling common factors?

We can simplify rational expressions by canceling common factors in the numerator and the denominator. In this lesson, you will learn how to multiply rational expressions. To start, let?s recall how to multiply numerical fractions. In conclusion, to multiply two numerical fractions, we factored, canceled common factors, and multiplied across.

How to divide two fractions by a rational function?

Multiply the functions and then simplify the result. To divide two fractions, we multiply by the reciprocal of the divisor. Dividing rational expressions is performed in a similar manner. In general, given polynomials P, Q, R, and S, where Q ? 0, R ? 0, and S ? 0, we have

Can you polish scratches out of prescription glasses?

All you need is a non-abrasive and non-gel based toothpaste. Put a dollop of toothpaste on the scratched area of glasses and gently rub it in soft circular motions by using a cotton ball or cloth. Keep rubbing in small circular motions for a few seconds and see the scratches vanish.

How do you get scratches out of eyeglass lenses?

Mix one to two tablespoons of baking soda with warm water until it forms a thick paste. Apply the baking soda-water mixture directly to the scratched part of your lenses using a cotton ball or a clean microfiber cloth. Use a consistent, circular motion and gentle pressure without pushing down too hard.

Can an optometrist fix scratched glasses?

Can a professional help with eyeglass scratches?

In terms of repair, probably not. Katsikos doesn?t advise going to an optician or optometrist to try to fix a small scratch. Chances are, they won?t be able to get rid of small scratches.

How does baking soda remove scratches from glasses?

You can combine 1-2 teaspoons of baking soda and a small amount of water to create a thick homemade paste that is known to work just as well. As with toothpaste, use a microfiber or cleaning cloth to apply paste to dry lens in a circular motion. Rinse and dry with a clean microfiber towel.

How does toothpaste remove scratches from glasses?

Toothpaste marketed as non-abrasive still contains a small amount of an abrasive component, in order to be effective for cleaning the teeth. This abrasive component gently removes a thin layer of plastic from the lens, thus leveling out the surface and removing scratches.

Can you buff scratches out of polycarbonate lenses?

Rub the toothpaste onto the scratched surface of the polycarbonate lens in a circular motion for ten to twenty seconds. Step 3: Dampen a clean, soft, cotton cloth in cool water. Immediately wipe the wax off with a clean, soft, cotton cloth. Buff the lenses with an unsoiled portion of the cloth.

How do you remove haze from glasses?

Put one drop of dish soap into your mixed solution of water and isopropyl alcohol. Cap your bottle and swirl its contents gently to infuse the solution with soap. Apply your cleaner and wipe away the clouds. Spray a moderate amount of your lens cleaner onto each lens.

What should I use to polish my glasses?

This handy video shows us how to polish your glasses lenses using two cheap and convenient household products, metal polish and rubbing alcohol. Choose a low abrasive metal polish and use it to buff away at each scratch. Remember that it will take a while to polish out the product, so keep persevering!

What should I not use to clean my eyeglasses?

DON?T use household glass or surface cleaners to clean your eyeglasses. These products have ingredients that can damage eyeglass lenses and coatings, such as anti-reflective coating. DON?T use paper towels, napkins, tissues or toilet paper to clean your lenses.

How often should I Polish my eyeglasses at home?

This will usually cover wear and tear on the lenses for up to a year. Ask your vision specialist for a professional cleaning. He might use ultrasonic cleaners that can get out embedded dirt and give your glasses a professional polish. Continue to polish at home regularly.

Can you put plastic lens glasses back on?

Put your glasses back on! You should be able to see much better through your newly repaired lenses. Verify that your lenses are plastic, not glass. This method can ONLY be used on plastic lenses, as it will permanently and irrevocably ruin glass lenses.